Keywords/Coding
4.3.5 Using Nvivo
The magnitude of the errors fro a ensor wh discrete eleraents is sensitive to the exact position nd orientatio o a oNect's image within te pixel arrivy.
Small hanges n mage position can ]igure -,, large effect on the error. Errors were
es tiniated by calculating sample standard devicit t ions of randomly oriented ii-nages within sonie orientation range (either a 25 or degree range). Sample statistics front 30 trials i each range were calculated ad used as bases for con-tparisons.
§3.2: Locating Objects from Range Data 89
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Figure 3.3:_TWodjm64 st te accuracy of the part locating algorithms. a) Pan image. b) Rectangle image. c) Ellipse image
Sensitivity to Image Size
In evaluating the fitted boundary technique, measurements were interpolated from a table consisting of 6 equally spaced entries from to 10 degrees (I degree in-crements). The pan image was used in the evaluation. After the interpolation table was constructed the imaae was oriented precisely in the range from to 0 degrees. Contour data was generated from the sensor model and the resulting dis-crete image was evaluated to get an estimate of part position. This estimate was then compared to the actual part position and the difference was recorded. The length was varied (the aspect ratio is kept constant) and the errors in measured orientation recorded. Errors in orientation as a function of image length are shown' in Figure 0.4.
The feature locating technique was evaluated as follows. A randomly oriented image (within a range of to 10 degrees) of a straight line portion of an object was located by least squares line fitting data from the sensor model. Differences in orientation between the measured and actual orientation were recorded for different length edge images. Results are shown in Figure 413 in Section 43.
Although the results (standard deviations of errors in orientation) from the fitted boundary interpolation technique appear to be quite inferior to the results
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Fig-Lire 34: Dependence of te fitted botindary interpolatimi algorithin on the lirnigth of -,tn in-tage of it pan w1iose orientation is betweeit 5 and 10 dgrees
of the feature locating technique, they fire extreltiely sensiti-w! to thC iD. Cerpolation Cable dcmsit-Y (see Figure 32). In the limit of i-t ft,11y s,-,thirated Cable, the fittedA
&-Amd-,iry intexpolation table has explicit vlues for all dis(-,.Cet,-- RN'tges a.td gives e.13111ts of eual or g.Leater accurate than the featim- locating approach. Vari-i - -es which deteradne the accuracy of the fitted bonn'tary ii-iterpolation technique -vvith sub-satuxation table densities are discussed in subsequent sections.
Image Orientation
The accuracy of te fitted boundary interpohation algorithm ;as unction of iniage ori(--,-ntation ws investigated I tbis test statistics from 30 trials i each degree range fron 0 to 65 dgrees were collected. Orientation tables witih one egree incTem.ents for both the pan finlage &d the rectangle; i-Inage, wre sed. 1-niages of the an and sbsequently of th rctangle were presented to the sensor witb.in the working range of he tble. The results are shown i'Figures 35 ad 36.
Errors in orientation for te pan 'linage are larger and vary nior tan those for the rectangle iage. The decrease in accuracy wth increasing tingle as seen 'in the
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!'3.2: Locating Ob'ects from Range Data3 - .7
----Figure 35: Dc!pc-n('Iency of the fitted bound.ary interp6lation te.c.11D.ique with mage (:)rientation for J.'IMIge 0- r a pan
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Mg-ure 36: De-pendency of the fitted boundary nterp6lation tchnique with im,,,,tge Orientation for- image of a rectangle
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k-1/itapter 3 Part Position Sensing for Assembly 92
rectangle is due to the decrease in projected length of the image of the rectangle and to an increase in the number of discontinuities in the interpolation table as described later.
The accuracy of the feature locating technique as a function of feature orienta-tion is the same as the accuracy of the linear least squares technique (see Figure 41.0 in Section 4.3)_
The rectangle interpolation table with I degree increments was sufficiently fine to produce errors which were comparable to those of the feature locating (least squares line fitting) technique while the pan table with degree increments pro-duced errors to 10 times greater than the feature locating technique.
Image Shapes
The errors in locating an image using the fitted boundary interpolation technique can change more than an order of magnitude depending upon the shape of te object. The closer the shape of the object is to a straight line, the better the performance of the algorithm. This conclusion is supported by the fact that the method more accurately locates the rectangle than it does the pan (Figures 35 and 3.6 and Section 32.3). Rectangles and ellipses with large aspect ratios are more accurately located than similarly shaped images with aspect ratios approaching I (Figures 37 and 38). This shape dependence 'is due to the number and magnitude of the discontinuities in the orientation tables. Comparing the number of discon-tinuities in the table generated for the pan image (aspect ratio 2 - Figure 39) to the tables for ellipses and rectangles of various aspect ratios (Figures 310 and 3.11), we may conclude that the longer and straighter the object, the higher the accuracy of the fitted boundary technique. Only the first part of the interpo-lation table (where the table was single valued) was used. Table interpointerpo-lation of orientations above about 65 degrees were not performed.
The discontinuities in the interpolation table are an artifact of the discretization of the image. At certain positions, small rotations of an object may change only a few pixels states; alternatively, a large number of pixels may change state. If subsequent small rotations of the object (in the same direction) during the learning phase of the fitted boundary technique generate very few pixel state changes then a large nmber of pixel state changes, a discontinuity in the interpolation -table will result. Since the pixel state changes may appen simultaneously, a very fine
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§,9.2: Locating Objects from Range Data 93
Figure 37: Dependence of the fitted bound-ary interpolation technique on te as-pect rtio of a rectangular image
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Fgure 38: Dependence of the fitted boundary interpolation technique on the as-pect rtio of n elliptical image
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IOllapter 9: Part Position Sensing for Assembly 94
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§ 3.2: Locating Objects from Range Data 95
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Orientation (Do rees) Ellipse Table with an Aspe t Ratio 2
Figure 311: Tables for ellipses of various aspect ratios
interpolation table may also exhibit many discontinuities. Figure 312 shows the quantized outline of an ellipse. A small rotation, 6a, of the ellipse can bring about a relatively large rotation in the line fitted to the upper boundary of the ellipse due to the change of state of a number of the pixels on the right and left boundaries. This change in the fitted line orientation results in a discontinuity in the interpolation
table.
Since the feature locating technique studied herein is only capable of locating straight line features, it will not be discussed in this section.