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CADDIT Guide:
CADDIT Guide:
Overview of Mathcad 14.0 basics
Overview of Mathcad 14.0 basics
& Industry Specific Features.
& Industry Specific Features.
Contents
Contents
Mathcad -
Mathcad - Exploring the possibilities...
Exploring the possibilities...
...3
...3
Mathcad – “Jack of
Mathcad – “Jack of all trades”...
all trades”...
...4
...4
Using Mathcad – Beginner’s Overview
Using Mathcad – Beginner’s Overview ...
...
...
...6
6
Inserting Text, functions, values and changing the unit system
Inserting Text, functions, values and changing the unit system ...
...
...
...
... 6
6
Errors and solution checking for calculations
Errors and solution checking for calculations ...
... ...
... 7
7
Entering Characters and other functions using shortcuts
Entering Characters and other functions using shortcuts ...
...
...
...
...
...
... 8
8
Graphing
Graphing ...
... ...
... ...
... 8
8
Integrating Mathcad with PTC Pro/Engineer
Integrating Mathcad with PTC Pro/Engineer ...
... ...
... 11
11
Mathcad Librar
Mathcad Libraries and Extens
ies and Extension Packs
ion Packs ...
...13
...13
Mathcad Engineering Libraries
Mathcad Engineering Libraries ...
... ...
... 13
13
Mathcad Extension Packs
Mathcad Extension Packs ...
... ...
... ...
... 13
13
Industry Specific Examples
Industry Specific Examples ...
...
...14
...14
Chemical Analysis
Chemical Analysis ...
... ...
... ...
... 14
14
Medical Imaging and Nuclear Medicine
Medical Imaging and Nuclear Medicine ...
... ...
... 18
18
Preconditioning Data
Preconditioning Data ...
... ...
... ...
... 29
29
Descriptive Statistics
Descriptive Statistics ...
... ...
... ...
... 34
34
Index
Index ...
...
...
...39
...39
Mathcad - Exploring the possibilities
Mathcad - Exploring the possibilities
Let’s journey back to a time before all our f
Let’s journey back to a time before all our f ancy electronicancy electronic gizmos and time saving devices, to a
gizmos and time saving devices, to a time where maths was muchtime where maths was much simpler and counting was done simply with the use of
simpler and counting was done simply with the use of our fingers or aour fingers or a tally stick. As record keeping methods and arithmetic developed so did tally stick. As record keeping methods and arithmetic developed so did our use of tools such
our use of tools such as the abacus particularly in parts of Asia andas the abacus particularly in parts of Asia and Africa. The abacus was in use centuries before we a
Africa. The abacus was in use centuries before we a dopted the writtendopted the written modern numeral system.
modern numeral system.
We have since then had m
We have since then had many technological advancesany technological advances beginning with the invention of
beginning with the invention of the calculator. Now imagine life withoutthe calculator. Now imagine life without
calculators, not only would calculations be much more difficult to compute but calculators, not only would calculations be much more difficult to compute but more advanced calculations would also occur at a snails pace. T
more advanced calculations would also occur at a snails pace. T hink of thehink of the implications in fields such as m
implications in fields such as m athematics, science, engineering, business,athematics, science, engineering, business, and aerospace just to name a fe
and aerospace just to name a fe w. There would have been obvious limitationsw. There would have been obvious limitations placed on the growth and development within these fields.
placed on the growth and development within these fields. Further advances have since occurred in the
Further advances have since occurred in the field of softwarefield of software to help cope with the very real and
to help cope with the very real and present demand for a mathematicalpresent demand for a mathematical program that allows users to
program that allows users to perform, document, share calculations andperform, document, share calculations and design work. Mathcad was first introduced in 1986 and
design work. Mathcad was first introduced in 1986 and is the first and only engineeringis the first and only engineering calculation software that automatically computes and d
calculation software that automatically computes and d ocuments engineering calculations whileocuments engineering calculations while dramatically reducing the risk of costly errors.
dramatically reducing the risk of costly errors. Mathcad version 14.0Mathcad version 14.0is now the global standard inis now the global standard in engineering calculation.
engineering calculation.
Mathcad is used by engineers, scientists and other technical professionals to Mathcad is used by engineers, scientists and other technical professionals to capture knowledge reuse calculations and encourage collaboration. Its unique visual format and capture knowledge reuse calculations and encourage collaboration. Its unique visual format and easy to use
easy to use scratchpad user scratchpad user interface (WYSIWYG) integrates standard mathematical notation,interface (WYSIWYG) integrates standard mathematical notation, text and graphs in a single
text and graphs in a single worksheet makes life simpler. Mathcad is superior to any proprietaryworksheet makes life simpler. Mathcad is superior to any proprietary calculating tool and spreadsheets in that it allows you to document, format and
calculating tool and spreadsheets in that it allows you to document, format and present your workpresent your work while simultaneously applying comprehensive mathematical functionality and dynamic, unit a while simultaneously applying comprehensive mathematical functionality and dynamic, unit a wareware calculations.
calculations.
PTC have coined the term “Engineering excellence” however this ebook is aimed PTC have coined the term “Engineering excellence” however this ebook is aimed at looking not only at the f
at looking not only at the f ield of engineering but the other possibilities that exist for Mathcad inield of engineering but the other possibilities that exist for Mathcad in other industries including the medical and scientific fields. Mathcad is not only easy to learn other industries including the medical and scientific fields. Mathcad is not only easy to learn butbut easy to use and
easy to use and does not require additional programming skills or training required for its use. It isdoes not require additional programming skills or training required for its use. It is able to increase productivity and improve verification and validation of calculations within a variety able to increase productivity and improve verification and validation of calculations within a variety of industries. Not only is it able to reuse c
of industries. Not only is it able to reuse c alculation content saving time and effort, Mathcad isalculation content saving time and effort, Mathcad is able to securely manage calculations and ensure a s
Mathcad – “Jack of all trades”
Mathcad – “Jack of all trades”
Mathcad is a mathematical "Jack of all trades" application for visual calculations in engineering, Mathcad is a mathematical "Jack of all trades" application for visual calculations in engineering, medicine, imaging, quality control, statistics, data analysis and
medicine, imaging, quality control, statistics, data analysis and transformation. Here are just a transformation. Here are just a fewfew examples of the fields for Mathcad application.
examples of the fields for Mathcad application.
Concept
Concept Field Field MathCAD MathCAD module module CommentsComments Quality Control
Quality Control Data analysisData analysis
-- Utilities andUtilities and descriptive descriptive statistics statistics
Quality control and quality engineering are use
Quality control and quality engineering are use d in developing systems to ensured in developing systems to ensure products
productsor or servicesservicesare designed and produced to meet or are designed and produced to meet or exceed customer exceed customer requirements. It deals with assurance and failure testing
requirements. It deals with assurance and failure testing in design and production of in design and production of products or services, to meet or
products or services, to meet or exceed customer requirements. Therefore it is anexceed customer requirements. Therefore it is an extremely important aspect in the manufacturing process and er
extremely important aspect in the manufacturing process and er rors can result in loss rors can result in loss of of productivity, time and money. Mathcad can help to accelerating products to
productivity, time and money. Mathcad can help to accelerating products to market,market, reducing costs and eliminating the risk
reducing costs and eliminating the risk of design failures.of design failures.
Chemical analysis
Chemical analysis Data analysisData analysis
-- PreconditioningPreconditioning data and data and interpolation interpolation
Chemical analysis deals with the central tasks
Chemical analysis deals with the central tasks of finding out the identity of an unknownof finding out the identity of an unknown substance, determining its properties and structure, isolating it from other c
substance, determining its properties and structure, isolating it from other c omponents,omponents, and detecting it and quantifying its amount in a
and detecting it and quantifying its amount in a given system.given system.
e.g. Water analysis, metal detection, assay & purity testing, spectroscopy, titration, e.g. Water analysis, metal detection, assay & purity testing, spectroscopy, titration, nuclear magnetic resonance.
nuclear magnetic resonance.
http://science.widener.edu/~svanbram/mathcad.html http://science.widener.edu/~svanbram/mathcad.html Civil and Civil and environmental environmental Engineering Engineering Data
Data analysis analysis e.g. e.g. When When comparing comparing two two different different materials materials the the Wilcoxon Wilcoxon Signed-Rank Signed-Rank Test Test can can bebe used to find to some degree
used to find to some degree the statistical significance, whether the means of twothe statistical significance, whether the means of two different data sets are equal, i.e. if they came
different data sets are equal, i.e. if they came form the same distribution.form the same distribution.
Signal/ waveform Signal/ waveform preconditioning preconditioning Data analysis Data analysis -- MeanMean smoothing smoothing -- CosineCosine smoothing smoothing
Many of today’s applications require measuring, or
Many of today’s applications require measuring, or creating a precise signal in a creating a precise signal in a veryvery noisy environment. This may require the use of
noisy environment. This may require the use of smoothingsmoothingfilters however some built-infilters however some built-in filters tend to over-smooth
filters tend to over-smooth data, removing important features. MathCAD allows for data, removing important features. MathCAD allows for greater control in order to
greater control in order to obtain the desired level of filtering required for a sobtain the desired level of filtering required for a s pecific task.pecific task. http://www.caddit.net/forum/viewtopic.php?p=771
http://www.caddit.net/forum/viewtopic.php?p=771
http://www.imakenews.com/ptcexpress/e_article001119634.cfm?x=bcR12Vy,b3jsqcsB,w
http://www.imakenews.com/ptcexpress/e_article001119634.cfm?x=bcR12Vy,b3jsqcsB,w
Astronomy
Astronomy Data Data analysis analysis Mathcad Mathcad can can also also have have applications applications in in the the field field of of astronomy. astronomy. For For example example it it can can bebe used to generate a s
used to generate a s et of orbital elements for the planet a planet et of orbital elements for the planet a planet that can be used tothat can be used to calculate its position at any instant of
calculate its position at any instant of the year. Orbital elements are a dynamicalthe year. Orbital elements are a dynamical astronomer's way of describing an
astronomer's way of describing an orbit in a manner that is useful for orbit in a manner that is useful for calculatingcalculating positions in the orbit
positions in the orbit E.g.
Medical imaging Medical imaging (Radiodiagnostics, (Radiodiagnostics, electron electron microscopy, microscopy, nuclear medicine) nuclear medicine) Imaging Processing Imaging Processing & & Wavelets Wavelets
Image processing and analysis can
Image processing and analysis can be used to clean images, remove distortions,be used to clean images, remove distortions, highlight important features, add colour,
highlight important features, add colour, image manipulation, manipulating colour,image manipulation, manipulating colour, combining images, zoom, enlarge, making images crisper, create
combining images, zoom, enlarge, making images crisper, create inverse images andinverse images and much more. It is also a
much more. It is also a means of extracting quantitative information from images as wellmeans of extracting quantitative information from images as well as a means of
as a means of detecting and measuring objects in images.detecting and measuring objects in images. http://www.caddit.net/forum/viewtopic.php?t=243
http://www.caddit.net/forum/viewtopic.php?t=243
Speech pathology
Speech pathology Imaging ProcessingImaging Processing &
&
Signal Processing Signal Processing
The Speech spectrogram module along with the Fourier
The Speech spectrogram module along with the Fourier transformations module can betransformations module can be used in the area of
used in the area of Speech Pathology to analyse abnormal speech Speech Pathology to analyse abnormal speech patterns.patterns.
Forensics & Forensics & Security Security
Wavelets
Wavelets Fingerprint Fingerprint recognition recognition or or fingerprint fingerprint authentication authentication refers refers to to thethe automatedautomatedmethod of method of verifying a match between two human
verifying a match between two human fingerprintsfingerprints. Wavelets are particularly useful in. Wavelets are particularly useful in compressing digitised fingerprints. Wavelet methods were selected as part of
compressing digitised fingerprints. Wavelet methods were selected as part of an FBIan FBI standard for compression of fingerprint images.
standard for compression of fingerprint images. http://www.afp.gov.au/national/e-crime/forensics.html
Using Mathcad – Beginner’s Overview
Using Mathcad – Beginner’s Overview
H
Here’s a basic introduction to some of ere’s a basic introduction to some of the tools and applications available in Mathcad.the tools and applications available in Mathcad.
Note: For help on installing Mathcad for the first time, click
Note: For help on installing Mathcad for the first time, click HERE HERE ..
Now, as we start
Now, as we start MathcadMathcad software, a window as the one shown here should appear. On thissoftware, a window as the one shown here should appear. On this
Image, each area of the window is labelled for your consideration as we walk through the
Image, each area of the window is labelled for your consideration as we walk through the
workspace or window in which you will be working in.
workspace or window in which you will be working in.
The drop menus are the
The drop menus are the list of menus in which you can find list of menus in which you can find various commands to math,various commands to math,
graphics symbolic options to use in Mathcad as
graphics symbolic options to use in Mathcad as well as the various functions of editing andwell as the various functions of editing and
controlling your worksheets that you will working with. The Insert, Format and Symbolics menus
controlling your worksheets that you will working with. The Insert, Format and Symbolics menus
are the most commonly used drop menus
are the most commonly used drop menus to gain access to the different mathematical function atto gain access to the different mathematical function at
your disposal with Mathcad.
your disposal with Mathcad.
As we go down further in
As we go down further in the image from the drop menus, there are list of the image from the drop menus, there are list of icons where are allicons where are all
shortcuts various and commonly used functions in Mathcad. This is k
shortcuts various and commonly used functions in Mathcad. This is known as thenown as themain toolbar main toolbar ..
Here you can save, cut, paste, change
Here you can save, cut, paste, change fonts and sizes and other various ffonts and sizes and other various functions as well. Under unctions as well. Under
the main toolbar is the math palette. Here is a
the main toolbar is the math palette. Here is a set of shortcut icons of just a set of shortcut icons of just a few of the manyfew of the many
functions that are with Mathcad. Note to take is that b
functions that are with Mathcad. Note to take is that by clicking on any of the icons in the y clicking on any of the icons in the mathmath
palette will open an additional dialogue box which will allow you to use
palette will open an additional dialogue box which will allow you to use the various options arethe various options are
made available to you. In addition to that, there is
made available to you. In addition to that, there is also a control palette that allowsalso a control palette that allowsObject LinkingObject Linking and Embedding (OLE)
and Embedding (OLE). This means that you can . This means that you can integrate various items from other programs tointegrate various items from other programs to
be added to
be added to your worksheet in the calculation process. However it is required that you need toyour worksheet in the calculation process. However it is required that you need to
understand a degree of scripting before
understand a degree of scripting before you undertake using this function.you undertake using this function.
Next is the workspace in which will be doing the
Next is the workspace in which will be doing the layout out of the calculations as well aslayout out of the calculations as well as
various descriptions and information to be placed in. At very bottom
various descriptions and information to be placed in. At very bottom of it all there is a smallof it all there is a small
section known as the message box. T
section known as the message box. This box will tell you what description of the function youhis box will tell you what description of the function you
have selected.
keyboard or using the calculator icon located in the m
keyboard or using the calculator icon located in the math palette. By entering an equal sign after ath palette. By entering an equal sign after
the calculation, Mathcad will give a solution. By adding different units in the previous equation by
the calculation, Mathcad will give a solution. By adding different units in the previous equation by
simply re-clicking the area in which the equation is entered, will allow for Mathcad to recalculate
simply re-clicking the area in which the equation is entered, will allow for Mathcad to recalculate
the answer in units for you. To
the answer in units for you. To change the units in the final answer, just simply double click thechange the units in the final answer, just simply double click the
unit and a dialogue will open up
unit and a dialogue will open up to allow you to select the various units which are to allow you to select the various units which are available inavailable in
Mathcad. Depending on the version you h
Mathcad. Depending on the version you have, the European version will have the units based onave, the European version will have the units based on
the SI system, however you can change to
the SI system, however you can change to imperial system or US system by going to the dropimperial system or US system by going to the drop
menu> select tools > Worksheet options >select the U
menu> select tools > Worksheet options >select the Unit system tab and selecting the desirednit system tab and selecting the desired
unit system.
unit system.
Mathcad also has a list of
Mathcad also has a list of various functions which you can simply access by going to various functions which you can simply access by going to the dropthe drop
menu > insert > function. This will open a
menu > insert > function. This will open a dialogue as shown here, allowing you to accdialogue as shown here, allowing you to access a largeess a large
variety of functions which are used in mathematics, engineering and
variety of functions which are used in mathematics, engineering and other fields requiringother fields requiring
calculations.
calculations.
You can also move singular or multiple calculations on the workspace, by h
You can also move singular or multiple calculations on the workspace, by holding the leftolding the left
mouse button and dragging a
mouse button and dragging a box highlighting the calculations. You will notice that a hand willbox highlighting the calculations. You will notice that a hand will
appear over the box highlighted allowing you to m
appear over the box highlighted allowing you to move calculations freely in the workspace. Byove calculations freely in the workspace. By
using the Shift key, you can deselect various
using the Shift key, you can deselect various parts of the calculations that you do not parts of the calculations that you do not want towant to
move.
move.
Errors and solution checking for calculations
Errors and solution checking for calculations
Algebraic expressions can also be entered into Mathcad and
Algebraic expressions can also be entered into Mathcad and then able to generate a then able to generate a solutionsolution
with given values. Firstly, this is done by entering the expression, and t
with given values. Firstly, this is done by entering the expression, and then above it entering thehen above it entering the
values of the various terms show in the
values of the various terms show in the equation. Note that if the equation is showing someequation. Note that if the equation is showing some
highlighted parts of the equation, this tells the user that
highlighted parts of the equation, this tells the user that he or she has not he or she has not entered the necessaryentered the necessary
values to work out the solution to the e
values to work out the solution to the equation. Mathcad provides an answer to the highlightedquation. Mathcad provides an answer to the highlighted
error in the calculation by click on the error itself. A small description will be given. Note to
error in the calculation by click on the error itself. A small description will be given. Note to
remember is when entering expressions use the colon
remember is when entering expressions use the colon key Shift+ [:] and when giving a value usekey Shift+ [:] and when giving a value use
For example, In the image below you can
For example, In the image below you can see what Mathcad has Identified a problem with mysee what Mathcad has Identified a problem with my
calculation of y here. I haven't given the
calculation of y here. I haven't given the value for b within the calculations and shown in the value for b within the calculations and shown in the nextnext
image the problem is identified as soon as I
Entering Characters and other functions using shortcuts
Entering Characters and other functions using shortcuts
A lot of the functions have been
A lot of the functions have been arranged intoarranged intoshortcutshortcutkeyskeys. Example of this is the Greek. Example of this is the Greek
characters which are most commonly used in engineering equations and c
characters which are most commonly used in engineering equations and calculations. With Other alculations. With Other
programs such as excel will require for you to
programs such as excel will require for you to go to the character maps go to the character maps and select the individualand select the individual
and then insert them into the field, cut and
and then insert them into the field, cut and paste the expression into the desired equation.paste the expression into the desired equation.
Mathcad has provided the shortcut within in the Math palette where
Mathcad has provided the shortcut within in the Math palette where you can add the charactersyou can add the characters
individually or by pressing Ctrl and keystroke g to change t
individually or by pressing Ctrl and keystroke g to change the previous character entered into ahe previous character entered into a
Greek character. Example of this is the
Greek character. Example of this is the pi pi symbol. To create the character symbol. To create the character pi pi , you just have t, you just have typeype
the letter p and then ctrl+g to
the letter p and then ctrl+g to change it π or alternatively use ctrl+shift+p to get the change it π or alternatively use ctrl+shift+p to get the symbol of symbol of pi pi ..
This is only one example of
This is only one example of the various keyboard shortcuts which can be found the various keyboard shortcuts which can be found in drop menu helpin drop menu help
> quick sheets > ke
> quick sheets > keyboard shortcuts.yboard shortcuts.
Graphing
Graphing
Graphing of various points can be
Graphing of various points can be done differently depending on the values which are used done differently depending on the values which are used asas
well as the function which is used to
well as the function which is used to generate the graph. Now by creating a table generate the graph. Now by creating a table of values (doneof values (done
by right clicking within the workspace >insert table), you can use this to
by right clicking within the workspace >insert table), you can use this to define your graph. Firstlydefine your graph. Firstly
you will need to enter in the
you will need to enter in the values in the appropriate fields as shown in tvalues in the appropriate fields as shown in this example. Once youhis example. Once you
have completed this, the next step will require for you to
have completed this, the next step will require for you to define the table. In this case, we willdefine the table. In this case, we will
define the table as T. Next we
define the table as T. Next we will have to define the X and will have to define the X and Y axis in which values we will beY axis in which values we will be
using. By typing x, : m
using. By typing x, : m [ctrl+6], 0, this will give the following function of x:= m[ctrl+6], 0, this will give the following function of x:= m00. This will tell. This will tell
Mathcad to use the values found in column 0 as the x values. The process is repeated to the y
Mathcad to use the values found in column 0 as the x values. The process is repeated to the y
-axis by replacing the x with y a
axis by replacing the x with y and 0 with 1 giving the fund 0 with 1 giving the function of y:= mnction of y:= m11..
You can also sketch graphs based on
You can also sketch graphs based on data collected by using the matrix function as data collected by using the matrix function as well towell to
define the values given. This is done
define the values given. This is done by entering the name by entering the name of the data and then by of the data and then by pressingpressing
[Ctrl+M] to open the matrix option. Next define the amount of values which will be
[Ctrl+M] to open the matrix option. Next define the amount of values which will be entered andentered and
enter the data required. For example: the values
enter the data required. For example: the values for X axis can be called xdata for X axis can be called xdata and pressingand pressing
[shift+colon] and then [ctrl+M] to generate the matrix. Next is just adjusting the am
Once the values of
Once the values of the X and Y axis has been complete, either go to the drop menu insert andthe X and Y axis has been complete, either go to the drop menu insert and
then graph and then X,Y plot or
then graph and then X,Y plot or go to the Math palette, graph icon go to the Math palette, graph icon and then x, y plot icon. and then x, y plot icon. This willThis will
give you a graph which look
give you a graph which looks like the following image:s like the following image:
You will need now to define the X an
You will need now to define the X and Y axis by clicking on the Axis Labed Y axis by clicking on the Axis Label under the x axis andl under the x axis and
type x to set the X
type x to set the X axis and repeat for the axis and repeat for the y axis in a similar fashion. Once you have done y axis in a similar fashion. Once you have done this,this,
click outside the graph box to generate the
click outside the graph box to generate the graph. You can adjust the upper graph. You can adjust the upper and lower limits of and lower limits of
the x and y
the x and y axis values by clicking within the box and changing the axis values by clicking within the box and changing the values near to the limits of thevalues near to the limits of the
axis as indicated here. The Graph can
axis as indicated here. The Graph can also be formatted based on preference of also be formatted based on preference of colour, style ascolour, style as
well showing the gridlines on graph. This is accessed b
well showing the gridlines on graph. This is accessed by right clicking on the graph area ay right clicking on the graph area andnd
selecting the format option. Here you will gain additional dialogue were you can c
selecting the format option. Here you will gain additional dialogue were you can change thehange the
format of the graph to better present the
format of the graph to better present the values to your liking.values to your liking.
Going back to the insert text option, various points of
Going back to the insert text option, various points of the graph can also be the graph can also be labelled andlabelled and
information can be given specific area of the graph. T
information can be given specific area of the graph. This can be performed by using the his can be performed by using the insertinsert
text function outside of the graph and
text function outside of the graph and then selecting the text or label and placing it then selecting the text or label and placing it on the graphon the graph
as desired. This is another function which allows for the
as desired. This is another function which allows for the Mathcad user to perform simple and easyMathcad user to perform simple and easy
task of labelling the graphs properly to share
task of labelling the graphs properly to share views and ideas other people who are views and ideas other people who are lookinglooking
through the calculation.
Multiple algebraic expressions of various graphs can be placed a
Multiple algebraic expressions of various graphs can be placed all on a singular graph toll on a singular graph to
compare the differences between functions drawn up. This can
compare the differences between functions drawn up. This can be done by entering multiplebe done by entering multiple
algebraic by the y axis and
algebraic by the y axis and ensuring that the expressions are still using the same ensuring that the expressions are still using the same x values. For x values. For
example as shown here, we can
example as shown here, we can see that the all the expressions which are used see that the all the expressions which are used here are labelledhere are labelled
different yet still use the same variable (x). Note: When entering in the
different yet still use the same variable (x). Note: When entering in the functions, ensure that thefunctions, ensure that the
functions used are separated by commas. F
functions used are separated by commas. For example: f(x),c(x),d(x)or example: f(x),c(x),d(x)
3D graphs can be gener
3D graphs can be generated in Mathcad by going to the ated in Mathcad by going to the graph palette and clicking on either graph palette and clicking on either
the surface, 3D bar, 3D vector graph icons. Entering an expression
the surface, 3D bar, 3D vector graph icons. Entering an expression which has more than onewhich has more than one
variable will generate the 3D graph. Integrating multiple expressions into the one 3D graph can
variable will generate the 3D graph. Integrating multiple expressions into the one 3D graph can
be done by using
be done by using the matrix function by entering the name of the matrix function by entering the name of the expression with the twothe expression with the two
variables, creating a matrix with rows and entering the values into the m
variables, creating a matrix with rows and entering the values into the matrix brackets. Changeatrix brackets. Change
the appearance of the 3D
the appearance of the 3D model is very much the same model is very much the same as the linear 2D graphs as well bas the linear 2D graphs as well by righty right
clicking and selecting the properties menu. A Note to remember
clicking and selecting the properties menu. A Note to remember is that the whole expression isis that the whole expression is
not required to be entered into the
not required to be entered into the graph since you can rgraph since you can refer the expression via assigned letter asefer the expression via assigned letter as
shown within this example.
Integrating Mathcad with PTC Pro/Engineer
Integrating Mathcad with PTC Pro/Engineer
Mathcad can be integrated into various programs
Mathcad can be integrated into various programs within PTC products. In this tutorial, we willwithin PTC products. In this tutorial, we will
be looking on how to integrate into
be looking on how to integrate into Pro Engineer via using the parameters as well as relationshipsPro Engineer via using the parameters as well as relationships
within the model in Pro/Engineer. Firstly, start of by creating a part that you
within the model in Pro/Engineer. Firstly, start of by creating a part that you want to use in prowant to use in pro
engineer. Here we have generated a C
engineer. Here we have generated a Cylinder for this example. Once completed, we go to the topylinder for this example. Once completed, we go to the top
of the menu and go
of the menu and go to tools/ parameters. Next we enter a new parameter, rename the to tools/ parameters. Next we enter a new parameter, rename the parameter parameter
to an appropriate name and then
to an appropriate name and then add a Value. Next, move to the add a Value. Next, move to the right hand side of the menu andright hand side of the menu and
insert the units for the height.
insert the units for the height.
Click okay to confirm. Next, go to top menu
Click okay to confirm. Next, go to top menu to analysis / external analysis and then to Mathcadto analysis / external analysis and then to Mathcad
analysis, this will open a new dialogue as shown b
analysis, this will open a new dialogue as shown below. At the top of the dialogue, you elow. At the top of the dialogue, you can loadcan load
previously made Mathcad worksheets or generate a ne
previously made Mathcad worksheets or generate a new worksheet to be used in the w worksheet to be used in the analysis.analysis.
Click new and a new worksheet for Mathcad
Click new and a new worksheet for Mathcad will open. To create a link from Mathcad towill open. To create a link from Mathcad to
Pro/Engineer, it is necessary to use the subscript here in the
Pro/Engineer, it is necessary to use the subscript here in the expressions that are written out. Weexpressions that are written out. We
linked the subscripted height value back to
linked the subscripted height value back to the word height to make sure that Mathcad isthe word height to make sure that Mathcad is
processing it to the correct value. W
processing it to the correct value. We also added an extra line here e also added an extra line here with height [=] to see if thewith height [=] to see if the
value is generated correctly. Next we need to link
value is generated correctly. Next we need to link the expressions to Pro/Engineer by going to thethe expressions to Pro/Engineer by going to the
properties to the first expression and then going to the
properties to the first expression and then going to the Tag Field and typeTag Field and type proe2mc proe2mc . This tells the. This tells the
program Pro engineer to get the input field from
program Pro engineer to get the input field from this Mathcad file. The Last Height Expression wethis Mathcad file. The Last Height Expression we
will use and go to properties, Tag
will use and go to properties, Tag and type mc2proe. This defines the output field from and type mc2proe. This defines the output field from MathcadMathcad
to Pro/Engineer model. Once completed Click save and name file accordingly.
to Pro/Engineer model. Once completed Click save and name file accordingly.
Now go back to Pro/Engineer to the Mathcad Analysis dialogue, click load an
Now go back to Pro/Engineer to the Mathcad Analysis dialogue, click load and select thed select the
Mathcad worksheet that you have created. Next, go
Mathcad worksheet that you have created. Next, go down the dialogue to add paramdown the dialogue to add parameter, selecteter, select
the name of the parameter that was created before a
the name of the parameter that was created before and next click the input field from Mathcadnd next click the input field from Mathcad
which was "
which was "Height_proeHeight_proe" and click okay. Exit the extra dialogue " and click okay. Exit the extra dialogue box and proceed to the box and proceed to the outputoutput
field box in the Mathcad analysis dialogue box. Select the
field box in the Mathcad analysis dialogue box. Select the ""height_proeheight_proe" output field defined in" output field defined in
Mathcad and to test, we will use the compute b
Mathcad and to test, we will use the compute button. Once that the value shows that it hasutton. Once that the value shows that it has
worked by giving the value we defined in
worked by giving the value we defined in parameters in this example, we click add feature, nameparameters in this example, we click add feature, name
the analysis accordingly and then save.
Next, go to relationship where we will need to define the
Next, go to relationship where we will need to define the relationship of the Height value on therelationship of the Height value on the
model with the Mathcad worksheet. To do this we
model with the Mathcad worksheet. To do this we go to the top menu go to the top menu tools / relations and type intools / relations and type in
the edge to work with, the expression to use
the edge to work with, the expression to use found in Mathcad and then found in Mathcad and then where the analysis iswhere the analysis is
located in the feature tree. An example is shown here
located in the feature tree. An example is shown here for the cylinder height.for the cylinder height.
Once completed, test the relationship to see if it is verified by Pro-Engineer and then
Once completed, test the relationship to see if it is verified by Pro-Engineer and then clickclick
regenerate. Note to remember is that if you change
regenerate. Note to remember is that if you change any values in the parameters after the many values in the parameters after the modelodel
has been regenerated you will have to c
has been regenerated you will have to click the regenerate button twice to complete the newlick the regenerate button twice to complete the new
changes. This is due to
changes. This is due to Pro-Engineer doing the first initial calculations but not displaying thePro-Engineer doing the first initial calculations but not displaying the
changes in the model. The second r
changes in the model. The second regeneration will regenerate the model that is shownegeneration will regenerate the model that is shown
graphically.
graphically.
These are just the few of
These are just the few of the features available with Mathcad that were shown in this Basicthe features available with Mathcad that were shown in this Basic
Tutorial. For additional information of the functions please refer to the tutorial in Mathcad as well
Tutorial. For additional information of the functions please refer to the tutorial in Mathcad as well
as the quick sheets to
Mathcad Libraries and Extension Packs
Mathcad Libraries and Extension Packs
Mathcad offers extensive, content-rich math libraries that
Mathcad offers extensive, content-rich math libraries that contain several well-known referencecontain several well-known reference books delivered as
books delivered as interactive e-books. These engineering discipline-specific libraries include:interactive e-books. These engineering discipline-specific libraries include:
Mathcad Engineering Libraries
Mathcad Engineering Libraries
Mathcad Civil Engineering Library Mathcad Civil Engineering Library Combines the encyclopedic “Roark’s Formulas fCombines the encyclopedic “Roark’s Formulas f or Stress and Strain” with easy-to-adaptor Stress and Strain” with easy-to-adapt structural design templates and examples of thermal design problems.
structural design templates and examples of thermal design problems. Mathcad Electrical Engineering Library
Mathcad Electrical Engineering Library
Provides hundreds of standard calculation procedures, formulae and reference tables used b Provides hundreds of standard calculation procedures, formulae and reference tables used b yy electrical engineers.
electrical engineers.
Mathcad Mechanical Engineering Library Mathcad Mechanical Engineering Library Combines the encyclopedic “Roark’s Formulas f
Combines the encyclopedic “Roark’s Formulas f or Stress and Strain” with easy-to-adaptor Stress and Strain” with easy-to-adapt calculations from a classic McGraw-Hill reference book,
calculations from a classic McGraw-Hill reference book, along with an interactive introduction toalong with an interactive introduction to the finite element method.
the finite element method.
Mathcad Extension Packs contain specialized libraries of functions designed to complement and Mathcad Extension Packs contain specialized libraries of functions designed to complement and extend Mathcad Professional's built-in function set. These extension packs expand Mathcad's extend Mathcad Professional's built-in function set. These extension packs expand Mathcad's capabilities while using standard Mathcad functions and operators. To extend the c
capabilities while using standard Mathcad functions and operators. To extend the c apabilities of apabilities of Mathcad into specific disciplines, four Mathcad
Mathcad into specific disciplines, four Mathcad Extension Packs are available:Extension Packs are available:
Mathcad Extension Packs
Mathcad Extension Packs
Mathcad Data Analysis Extension Pack
Mathcad Data Analysis Extension Pack
Enables engineers to easily import, manipulate and analyze data patterns and
Enables engineers to easily import, manipulate and analyze data patterns and relationships inrelationships in Mathcad.
Mathcad.
Mathcad Signal Processing Extension Pack
Mathcad Signal Processing Extension Pack
Offers more than 70 built-in signal processing functions, adding extensive capabilities for Offers more than 70 built-in signal processing functions, adding extensive capabilities for performing analog and digital signal
performing analog and digital signal processing, analysis and visualization.processing, analysis and visualization. Mathcad Image Processing Extension Pack
Mathcad Image Processing Extension Pack
Performs smoothing, crisping, edge detection, erosion and
Performs smoothing, crisping, edge detection, erosion and dilation algorithms on color anddilation algorithms on color and grayscale images–useful in medicine, astronomy, weather, geoph
grayscale images–useful in medicine, astronomy, weather, geoph ysics, geology, forensics andysics, geology, forensics and radar, among other fields.
radar, among other fields.
Mathcad Wavelets Extension Pack
Mathcad Wavelets Extension Pack
Facilitates a new approach to signal and image a
Facilitates a new approach to signal and image a nalysis, time series analysis, statistical signalnalysis, time series analysis, statistical signal estimation, data compression analysis and special numerical methods. Engineers can create an estimation, data compression analysis and special numerical methods. Engineers can create an almost limitless number of functions that duplicate any natural or abstract environment - useful for almost limitless number of functions that duplicate any natural or abstract environment - useful for compressing vast amounts of data, as in fingerprint identification or coding an MRI.
Industry Specific Examples
Industry Specific Examples
As mentioned previously, Mathcad has the capability to be tailored to the ne
As mentioned previously, Mathcad has the capability to be tailored to the ne eds of specificeds of specific industries or disciplines. Here are just a few examples of the types of
industries or disciplines. Here are just a few examples of the types of applications that Mathcadapplications that Mathcad can be used for.
can be used for.
Chemical Analysis
Chemical Analysis
(1) Why it is important it consider Mathcad? (1) Why it is important it consider Mathcad? (2) Working out on how to generate sta
(2) Working out on how to generate sta ndard curves with higher accuracy and using ndard curves with higher accuracy and using Mathcad to do the calculations
Mathcad to do the calculations
(3) Example Case of an Analysis of Dietary Metabolites in urine. (3) Example Case of an Analysis of Dietary Metabolites in urine.
Mathcad is a versatile and powerful mathematical program in which one can be
Mathcad is a versatile and powerful mathematical program in which one can be able to doable to do complex calculations and still be able to complete them in
complex calculations and still be able to complete them in a logical fashion. This is extremelya logical fashion. This is extremely useful in providing information that correlated among peers. This example will show how this can useful in providing information that correlated among peers. This example will show how this can be achieved.
be achieved.
Here we start with the data which is given and
Here we start with the data which is given and is processed into Mathcad by using is processed into Mathcad by using the Tablethe Table function which is assess accordingly by right clicking in the workspace and selecting insert----> function which is assess accordingly by right clicking in the workspace and selecting insert----> and the table.
and the table.
You may note that this example here is
You may note that this example here is done in duplicates to generate a mdone in duplicates to generate a m ore accurate resultore accurate result with the standard curve which is required for this assay m
with the standard curve which is required for this assay m ethod. Also it is good to notice that theethod. Also it is good to notice that the workspace can accommodate word or text anywhere within the calculations.
workspace can accommodate word or text anywhere within the calculations. Now we come down to the s
Now we come down to the second table which we have here with the econd table which we have here with the values which are taken outvalues which are taken out of the UV-Vis spectrometer. Take note to be able to us
of the UV-Vis spectrometer. Take note to be able to us e the figures later on in Mathcad, e the figures later on in Mathcad, you willyou will need to specify the columns that are
need to specify the columns that are used in the calculations later on. This is done used in the calculations later on. This is done by using theby using the following keys:
following keys: [x][:][space][m][des
Now we will specify the data points in which we will be
Now we will specify the data points in which we will be using, so in the next step using, so in the next step when doingwhen doing standard deviation calculations, the information is available. Now for the equation of standard standard deviation calculations, the information is available. Now for the equation of standard deviation can be shorthanded later by using a
deviation can be shorthanded later by using a SD(x) can be used later on within the worksheet.SD(x) can be used later on within the worksheet.
Now we can go to the
Now we can go to the insert function options to give us all the necessarinsert function options to give us all the necessar y equations or functionsy equations or functions that we require to do simple to complex statistics. This is done b
that we require to do simple to complex statistics. This is done b y going to the insert ---> functiony going to the insert ---> function and within the new dialogue on the left
and within the new dialogue on the left as shown here. We go as shown here. We go to statistics and select the requiredto statistics and select the required functions. Note also that every time you select another function within the right hand
functions. Note also that every time you select another function within the right hand windowwindow there is box underneath which gives u a
there is box underneath which gives u a description on what that function does as well as description on what that function does as well as thethe shorthand version of the function in Mathcad. This is
shorthand version of the function in Mathcad. This is valuable since you do not havaluable since you do not ha ve to comeve to come back to the the insert function over and
To save time you can se
To save time you can see that I am se that I am s imply cutting and pasting the functions here and editing theimply cutting and pasting the functions here and editing the values in which the function is to calculate. Simply click within the function where you want to values in which the function is to calculate. Simply click within the function where you want to editedit and enter in the new values.
and enter in the new values. Now in case the answer do not Now in case the answer do not automatically change with the newautomatically change with the new values given go to the top
values given go to the top of the menus and look of the menus and look for the calculate button as shown here or for the calculate button as shown here or alternatively by using the F9 key and this
alternatively by using the F9 key and this will perform the calculate function in Mathcad or Crtl F9will perform the calculate function in Mathcad or Crtl F9 to calculate the complete worksheet itself.
to calculate the complete worksheet itself.
Now after we have completed all the necessary calculations for the standard curve
Now after we have completed all the necessary calculations for the standard curve to be usedto be used her, we can start using the va
her, we can start using the va lues here to make our standard curved to lues here to make our standard curved to do our calculations. Go todo our calculations. Go to the Graph bar and select the
the Graph bar and select the x,y plot graph. Now to get the x,y plot graph. Now to get the values into the graph we just have tovalues into the graph we just have to click on the bottom middle box here an
click on the bottom middle box here an d enter in x and d enter in x and to the left middle box we add in to the left middle box we add in our our functions that we need which is the
functions that we need which is the y function as well as the r(x) which will give us the ly function as well as the r(x) which will give us the l ine of bestine of best fit. Now completed, to generate the graph simply click outside into the workspace.
fit. Now completed, to generate the graph simply click outside into the workspace.
You may notice that the axis of
You may notice that the axis of the graph are defined at a uthe graph are defined at a undesirable scale. To edit the scale,ndesirable scale. To edit the scale, click the graph once again and
click the graph once again and you will notice two of additional numbers which are part of theyou will notice two of additional numbers which are part of the graph on the bottom as
A new dialogue similar to the one show here will open
A new dialogue similar to the one show here will open and click on the options in the dialogueand click on the options in the dialogue under the x and y
under the x and y primary axis and un-tick auto grid and set to primary axis and un-tick auto grid and set to a desired amount of scale unitsa desired amount of scale units you would like. Once completed click apply and okay.
you would like. Once completed click apply and okay.
Now that we have the standard curve
Now that we have the standard curve we can start by working out the amwe can start by working out the am ount of urea in urineount of urea in urine sample, I am going to demonstrate how to integrate e
Medical Imaging and Nuclear Medicine
Medical Imaging and Nuclear Medicine
Mathcad has a broad range
Mathcad has a broad range of applications within the medical imaging field. Here’s another of applications within the medical imaging field. Here’s another example of how Mathcad can be ta
example of how Mathcad can be ta ilored to specific industry requirements.ilored to specific industry requirements. With all radiologist and
With all radiologist and radiographersradiographers, one thing they all k, one thing they all k now that is important is that the qualitynow that is important is that the quality of the images taken for the
of the images taken for the diagnostics must be of the highest quality possible. However, therediagnostics must be of the highest quality possible. However, there are many factors that contribute to poor quality image acquisition such as
are many factors that contribute to poor quality image acquisition such as parameters settings for parameters settings for the scan, image
the scan, image contrast, contrast sensitivity, distortion, noise as well as contrast, contrast sensitivity, distortion, noise as well as artifacts and blurring.artifacts and blurring. Getting that balance between sensitivity and selectivity creates the need for image processing a Getting that balance between sensitivity and selectivity creates the need for image processing a necessity.
necessity.
This example will allow for image processing possible to be done
This example will allow for image processing possible to be done in MathCAD, which can be usedin MathCAD, which can be used in the medical field where every little detail makes the difference in giving an
in the medical field where every little detail makes the difference in giving an accurate diagnosis.accurate diagnosis. We will focus on 5 process
We will focus on 5 processes in MathCAD to give quality images without comprising the integrityes in MathCAD to give quality images without comprising the integrity of the scans taken.
of the scans taken. 1. Equalisation 1. Equalisation
2. Function and level mapping 2. Function and level mapping 3. Noise and Error measurement 3. Noise and Error measurement 4. Crisping
4. Crisping 5. Filtering Noise 5. Filtering Noise
But why bother using Mathcad to do
But why bother using Mathcad to do image processing when other Photoshop programs areimage processing when other Photoshop programs are available? The answer is simple. Mathcad allows for far greater control on how
available? The answer is simple. Mathcad allows for far greater control on how defined you woulddefined you would like the image to be without comprising the image as
like the image to be without comprising the image as well as being able to customize usingwell as being able to customize using different algorithms. Also another factor to consider is that the images can be s
different algorithms. Also another factor to consider is that the images can be s wapped in and outwapped in and out quickly to use the same f
quickly to use the same function or that particular setting just by changing the address line whereunction or that particular setting just by changing the address line where the image is located.
the image is located.
First of all, we will be using an image which has
First of all, we will be using an image which has been provided through PTC for this tutorial. In thebeen provided through PTC for this tutorial. In the Handbook for image processing, the image which will be used to
Handbook for image processing, the image which will be used to demonstrate the variousdemonstrate the various features of the image processing pack in
features of the image processing pack in Mathcad is brain.gif as shown here. Through out thisMathcad is brain.gif as shown here. Through out this tutorial the original image is shown next to the edited image
tutorial the original image is shown next to the edited image which has been enhanced bywhich has been enhanced by MathCAD with appropriate names.
MathCAD with appropriate names.
Equalisation
Equalisation
Equalisation allows for the scanned image to be more defined b
Equalisation allows for the scanned image to be more defined b y controlling on how the light andy controlling on how the light and dark values are distributed in defined cumulative
dark values are distributed in defined cumulative histogramhistogramof the image. This will in turn create aof the image. This will in turn create a linear looking cumulative histogram of the scanned image and giving sharper d
linear looking cumulative histogram of the scanned image and giving sharper d etails on theetails on the image.
image.
Now to activate this function, command line typed out as equalize(M) , as
Now to activate this function, command line typed out as equalize(M) , as M is defined as your M is defined as your image from the previous line of calculation to this command. However it is best
Next I will output the image to a histogram
Next I will output the image to a histogram to see the degree of sto see the degree of spread of the intensities in thepread of the intensities in the 255 greyscale bands. Note that the
255 greyscale bands. Note that the number 256 is used since that number 256 is used since that the intensities start at andthe intensities start at and include 0 to 255, therefore giving 256
include 0 to 255, therefore giving 256 intensities). So the command of intensities). So the command of H:=imhist(M ,256)
H:=imhist(M ,256)
And for the histogram to work, we need to define
And for the histogram to work, we need to define the data in which the histogram will be usingthe data in which the histogram will be using which is the pixel matrix of the image as
which is the pixel matrix of the image as we defined as so:we defined as so: k:= 0..rows(H) – 1
k:= 0..rows(H) – 1
Next create a Histogram and define the axis accordingly to
Next create a Histogram and define the axis accordingly to the Hk as the function and k the Hk as the function and k as theas the axis values for x and
axis values for x and you should get a histogram like this:you should get a histogram like this:
Seeing the image is slightly dark, we will be spread out
Seeing the image is slightly dark, we will be spread out the intensities to define the features onthe intensities to define the features on the scan to help get a
the scan to help get a better detailed image of the scan. For this image, the better detailed image of the scan. For this image, the cumulative histogramcumulative histogram is given by the difference equation for C. So
is given by the difference equation for C. So we will define as the following and repeat the samewe will define as the following and repeat the same steps to create a cumulative histogram as shown with these steps.
steps to create a cumulative histogram as shown with these steps.
Cumulative histogram: Cumulative histogram:
Now that we can see the slope
Now that we can see the slope is not linear from the histogram, we will apply the equaliseis not linear from the histogram, we will apply the equalise function here to see what happens. W
The new cumulative histogram of equalized image generated by typing the
The new cumulative histogram of equalized image generated by typing the following commands:following commands:
Now just generate the
Now just generate the cumulative Histogram:cumulative Histogram:
Now as we can see the
Now as we can see the cumulative histogram is showing a relatively linear curve here give us thecumulative histogram is showing a relatively linear curve here give us the following images as a result.
Function and Level Mapping
Function and Level Mapping
Function and level mapping shows the different levels of intensities across an existing image Function and level mapping shows the different levels of intensities across an existing image which will allow for different areas of the image to be more
which will allow for different areas of the image to be more defined. This can be done to defined. This can be done to eliminateeliminate the amount of background noise as
the amount of background noise as we saw in the equalisation step for the first webinar.we saw in the equalisation step for the first webinar. To activate this function, type in funmap(M,f)
To activate this function, type in funmap(M,f) where M is the image matrix which needs to bewhere M is the image matrix which needs to be generated first. The character f in the command is f
generated first. The character f in the command is f or the function to be performed at each or the function to be performed at each vector vector or cells in the image matrix
or cells in the image matrix (256 levels to map the different intensities) which is going to be (256 levels to map the different intensities) which is going to be usedused to help define the details on the
to help define the details on the image.image. This means that every time that the image m
This means that every time that the image m atrix is processed by the new function, the mappingatrix is processed by the new function, the mapping image matrix will be also calculated with the new changes to the
image matrix will be also calculated with the new changes to the image at each intensity eachimage at each intensity each time separate as it is applied. To use
time separate as it is applied. To use this function, we type inthis function, we type in R
R := := READ_IMAREAD_IMAGE("C:\Program Files\Mathcad\Mathcad 14\Handbook\improc\brain.gif").GE("C:\Program Files\Mathcad\Mathcad 14\Handbook\improc\brain.gif"). This allows us to setup first variable for the function mapping. Next we
This allows us to setup first variable for the function mapping. Next we will use a function to helpwill use a function to help us generate the desired effect. Now there are a
us generate the desired effect. Now there are a number of other functions which can be number of other functions which can be used for used for this or custom made for their desired effect. However this will require doing some experimenting this or custom made for their desired effect. However this will require doing some experimenting and testing of the function applied to
and testing of the function applied to the image. For now we will be using the fthe image. For now we will be using the f ollowing function toollowing function to create the desired effect.
create the desired effect.
Here is a small list of possible functions which can be
Here is a small list of possible functions which can be used for the function mapping.used for the function mapping.
Once we have completed that we enter in Once we have completed that we enter in
fmap := Re(funmap(R,F)) fmap := Re(funmap(R,F))
Since that we have generated the function as
Since that we have generated the function as well the image matrix to use, using an output imagewell the image matrix to use, using an output image you can see the
Level Mapping
Level Mapping
Level Mapping allows for the replacement of the intensities with in a specified image b Level Mapping allows for the replacement of the intensities with in a specified image b y ay a specified area or vector of intensity. In other to simply put
specified area or vector of intensity. In other to simply put it, to increase the intensity levels withinit, to increase the intensity levels within a specific area by use a
a specific area by use a defined vector. An example of this can defined vector. An example of this can be said to be the be said to be the same of havingsame of having a 29th element in a
a 29th element in a vector will give a new level for the pixels with an intensity of vector will give a new level for the pixels with an intensity of 29. It is important29. It is important to note that images have entries within 0 and
to note that images have entries within 0 and the length of the vector used the length of the vector used of minus 1.of minus 1. An example of this is that we would like to create an
An example of this is that we would like to create an image with a squared intensity scale. Weimage with a squared intensity scale. We would create a Vector within:
would create a Vector within: r := 0 …255
r := 0 …255
This will result in the creation of the following curve constructed given us the
This will result in the creation of the following curve constructed given us the what the vector willwhat the vector will look like.
look like.
Now given by imaging pack we can
Now given by imaging pack we can use a number of examples as use a number of examples as shown here, to refine theshown here, to refine the image for better screening and printing resolution.
This therefore, helps in enhancing the image for better
This therefore, helps in enhancing the image for better diagnosis of the patient. Note to remember diagnosis of the patient. Note to remember is that a particular function map or look-up table can
is that a particular function map or look-up table can be created with monitor or sensor, whichbe created with monitor or sensor, which maps irregularities cause by the display to their corrected values.
maps irregularities cause by the display to their corrected values.
Once we are satisfied with the vector created we apply
Once we are satisfied with the vector created we apply the vector to the Level mapping functionthe vector to the Level mapping function with the following command and specify the image to be use
with the following command and specify the image to be use d in the level mapping as d in the level mapping as well.well. R
R := := READ_IMAREAD_IMAGE("C:\Program Files\Mathcad\Mathcad 14\Handbook\improc\brain.gif").GE("C:\Program Files\Mathcad\Mathcad 14\Handbook\improc\brain.gif"). level :=levelmap(R, vec)
level :=levelmap(R, vec)
Error and Noise Measurement
Error and Noise Measurement
With Error and Noise Measurement, we use functions which are based on
With Error and Noise Measurement, we use functions which are based on the relative error(the relative error( squared error ration, the mean squared error and
squared error ration, the mean squared error and the signal-to-noise ration between the twothe signal-to-noise ration between the two images which are used to be
images which are used to be compared. These functions are used to compared. These functions are used to determine the level of noisedetermine the level of noise that affects an image after that it is processed or
that affects an image after that it is processed or transmitted. To demonstrate this function we willtransmitted. To demonstrate this function we will be looking at a few examples
be looking at a few examples here.here.
Firstly we need to define out variables here: which are
Firstly we need to define out variables here: which are R that represents out first or control imageR that represents out first or control image matrix that we are using. And Q which is
matrix that we are using. And Q which is the second image matrix , the same sthe second image matrix , the same s ize as the first.ize as the first. Note that the functions return a number
Note that the functions return a number which represents the relative error, the mean squaredwhich represents the relative error, the mean squared error, or the
error, or the signal-to-noise ratiosignal-to-noise ratio(SNR) between M and Q. Remember that all returned values are(SNR) between M and Q. Remember that all returned values are in decibels (dB).
in decibels (dB).
Now the first of the three commands that we are
Now the first of the three commands that we are going to be looking at with error and going to be looking at with error and noisenoise measurement is the relative error. This function returns the squared error ratio over all the measurement is the relative error. This function returns the squared error ratio over all the elements of the two matrices that are defined by M
