Abstract— For reconstructing a surface in three dimensions, point clouds are used. Surface reconstruction helps to recreate the model of the object. The approximating surface from a given set of samples is called surface reconstruction. A surface is constructed by carefully selecting points from unorganized point clouds in three dimension space and can be converted into any geometrical shape by removing bad poles. An algorithm is used for the surface reconstruction from different point clouds in different geometrical shapes. The intented set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robustness in the presence of outliers. Power crust alogorithim is used to remove the bad poles and filteration is applied. The curve filtering and Point filtering is applied. Crust algorithm plays an important role due to its guaranteed quality of mesh generation. Crust algorithm monitors many parameters of mesh generation and examines the performance of the algorithm by calculating parameters. The main aim of the algorithm is to filter out insignificant data while preserving an acceptable level of output quality
Index Terms—About four key words or phrases in alphabetical order, separated by commas.
I. INTRODUCTION
Considering the areas of computer vision and computer graphics, 3D surface reconstruction is the course of capturing the shape and appearance of real objects. This process can be accomplished either by active or passive
methods. If the model is allowed to change its shape in time, this is referred to as non-rigid construction.
The research of 3D reconstruction has always been a complex goal to achieve. Using 3D reconstruction one can determine 3D profile of any object, as well as knowing the 3D coordinate of any point on the profile. The reconstruction of three-dimensional objects is generally regarded as scientific problem and core technology for a wide variety of fields, such as Computer Aided Geometric Design (CAGD), Computer Graphics, Computer Animation, Computer Vision, medical imaging, computational science, Virtual Reality, digital media, etc.
Active Methods
Active methods, i.e. range data methods, given the depth map, rebuild the 3D profile by numerical approximation approach and build the object in scenario based on model.
These methods actively interfere with the reconstructed object.
Passive Method
Passive methods of 3D reconstruction do not interfere with the reconstructed object; they only use a sensor to measure the radiance reflected or emitted by the object's surface to infer its 3D structure through image understanding. Typically, the sensor is an image sensor in a camera sensitive to visible light and the input to the method is a set of digital images (one, two or more) or video.
Surface reconstruction is the method of attaining three-dimensional complex surface model rapidly and
Image Reconstruction From Scattered Cloud Points Using Hybrid Filteration
Rumani Sharma*, Arun Bhatia**
*ECE, Kurukshetra University, Haryana, INDIA
**Lecturer of ECE, Kurukshetra University, Haryana, INDIA
Volume 6, Issue 11, November 2017 accurately from three-dimensional statistics collected as a
sample, and it is mostly used in reverse engineering.
Three-dimensional data gathered by measuring device is generally dense, so it is called Point Cloud data. Point cloud data are considered as an accumulation of the points in three-dimensional space, and every point cloud data has three co-ordinates x, y, z.
According to the various forms of data, point cloud data can be classified into two forms:
I. Ordered point cloud II. Scattered point cloud.
There is an approach for the reconstruction of a surface, and scalar fields defined over it, from scattered data points. The points are assumed sampled from the surfaces of a 3D object, and the sampling is assumed to be dense and uniform. Laser range scanners are capable of producing a dense sampling, usually organized in a rectangular grid, of an object surface.
Some models allow to measure the RGB components of the color (i.e. three scalar fields) at each sample point. When the object has simple shape, this grid of points can be an acceptable representation. However, objects with a more complex geometry, e.g. objects with holes, handles, pockets, cannot be scanned in a single pass, and the various scans are not easy to merge. Other applications, are like recovering the shape of a bone from contour data extracted from a CT scan, requires reconstruction of a surface from data points arranged in slices. The approach of considering the input points as unorganized are helpful of generating cross-derivatives by a uniform treatment of all spatial directions[20].
In High-quality reconstruction of geometry, a core goal is to capture detailed (or dense) 3D models of the real scene. Many systems based on real-time tracking, using sparse maps for localization rather than reconstruction. Other systems have used simple point based representations (such as surfels or aligned point clouds) for reconstruction. Kinect Fusion goes beyond these point-based representations by reconstructing surfaces, which more accurately approximate real-world geometry[14].
In some applications, other information derived from CAD models, measured values or GPS can also be used and integrated with the sensor data. . In active and passive sensors, four other methods for object and scene modelling can currently be classified :
(1) Image-Based Rendering (IBR): This method does not consider the generation of a geometric 3D model but, for specific objects and in view of specific camera motions and scene conditions, it might be taken as a good technique for the generation of virtual views. IBR creates novel views of 3D environments directly from input images. The Object discontinuities, especially in large-scale and geometrically complex environments, will change the output. Therefore, the IBR method is generally only used for operation that require limited visualisation.
(2) Image-Based Modelling (IBM): This is the method which is widely used for geometric surfaces of architectural objects or for precise terrain and city modeling. IBM methods (including photogrammetry) use 2D image measurements (correspondences) to recover 3D object information from a mathematical model or they obtain 3D data using methods such as shape from shading, texture, specularity, contour (medical applications) and shape from 2D edge gradients.
They are very compact and the sensors are often low cost.
(3) Range-Based Modeling: This method directly occupies the 3D geometric information of an object. It is based on costly (at least for now) active sensors and can produce a highly detailed and accurate representation of most shapes.
The sensors rely on artificial lights or pattern projection. In the past 25 years many advancements have been made in the field of solid-state electronics and photonics and many active 3D sensors have been developed. Nowadays many commercial solutions are available, based on triangulation (with laser light or border projection), time-of-flight, continuous wave, interferometry or reflectivity measurement principles.
(4) Combination Of Image-Based And Range-Based Modeling: Photogrammetry and laser scanning have been combined in particular for complex or large architectural objects, in which no technique by itself can be efficiently and quickly provide a complete and detailed model. Mostly the basic shapes such as planar surfaces are determined by image-based methods while the fine details such as reliefs employ range sensors[15].
1.5 SURFACE RECONSTRUCION PHASES
Surface Reconstruction phases has the following steps : Phase 1: Initial Surface Estimation
Phase 2: Mesh Optimization
Phase 3: Smooth Surface Optimization
Phase 1: Initial surface estimation: From an unorganized set of points, phase 1 creates an initial dense mesh. This phase evaluates the topology of the surface and generates an initial estimation of the geometry.
Phase 2: Mesh optimization: Initially the dense mesh generated in phase 1, phase 2 changes the number of faces by reducing them and improves the fitting to the data points.
This problem is formulated as optimization of an energy function that models the trade-off between the competing goals of accuracy, efficiency and preciseness. The number of vertices in the mesh, the connections between them, and their respective positions are taken as free variables in optimization.
Phase 3: Smooth surface optimization: In third phase, the surface representation is transformed from a piecewise linear one (meshes) to a piecewise smooth surface. A new piecewise smooth representation based on subdivision is now introduced. These surfaces are perfect for surface reconstruction because they are simple and easy to implement, models sharp features precisely and can be fitted using an extension of the phase 2 optimization[9].
Fig. 1 Surface Reconstruction phases
Various areas considered in Surface Reconstruction
Qualitative Properties
Active Illumination
Calibrated Environment
Uncalibrated Environments
An approach for the reconstruction of a surfaces is considered, and scalar fields defined over it, from scattered data points. The points are assumed to be sampled from the surface of a 3D object, and the sampling is considered to be dense and uniform.
Laser range scanners are able to produce a dense sampling, mostly organized in a rectangular grid, of an object surface.
Some models also helps to measure the RGB components of the color (i.e. three scalar fields) at each sampled point.
When the object has a simple shape, this grid of points can have a sufficient representation. However, objects with a more complex geometry, e.g. objects with holes, handles, pockets, cannot be scanned in a single pass, and the various
Volume 6, Issue 11, November 2017 scans are not easy to merge. Other applications include
restoring the shape of a bone from contour data extracted from a CT scan, require reconstruction of a surface from data points organized in slices. This approach of considering the input points as unorganized has the advantage of producing cross-derivatives by the equal treatment of all spatial directions[20].
II. LITERATURE REVIEW
Fabio Remondino, Sabry El-Hakim (2006) presented a full pipeline for 3D modelling from terrestrial image data, regarding the different approaches and analysing all the steps involved. The main problems and the available solutions are used for the generation of 3D models from terrestrial images.
Shivali Goel, Rajiv Bansal (2013) developed a system for image reconstruction from scattered cloud points. Crust algorithm with umbrella Filtering will be implemented.
Crust algorithm plays a vital role due to its guaranteed quality of triangular mesh generation. Crust algorithm monitors the various different parameters of mesh generation and evaluates the performance of the algorithm by calculating parameters. The main motive of the algorithm is to filter out left insignificant data while preserving an acceptable level of output quality.
Mincheol Yoon et. al. (2007) studied the suitability of ensembles for surface reconstruction. They experimented with a largely used normal reconstruction technique and Multi-level Partitions of Unity accurate for surface reconstruction, showing that normal and surface ensembles can be completely combined to handle noisy point sets.
Rajdeep Hooda, Anil Kamboj (2016) studied and analised various algorithms like crust algorithm, power algorithm and Delaunay algorithm compared for time taken by the algorithm for the surface reconstruction.
William Y. Chang (2007) studied techniques for reconstructing surfaces from points. He describe four main
ideas in the graphics literature: signed distance estimation, Voronoi-based reconstruction, implicit surface fitting, and moving least squares surfaces. The main challenges include reconstruction without surface normals, robustness to noise, accuracy to sharp features, and provable reconstruction guarantees.
Rajinder Singh (2015) discussed that virtual machines give users facility to run different operating system on the current operating system .With the help of Virtual Machines users can test the new versions of the software whether they fulfill the requirements or not. Virtual Machines also help to reduce the hardware cost of the computer system as one can follow the desired hardware needs. Main player of Virtual Machines are Virtua Box, VMware , QEMU, and Windows Virtual PC.
Two Virtual Machine software Virtual Box and VMware are discussed. Various Features of both the machines are also discussed.
Bernhard Reitinger et. al. developed a first prototype of a collective 3D reconstruction system for modeling urban scenes. An Augmented Reality scout is a person who is supplied with an ultra-mobile PC, an attached USB camera and a GPS receiver. The scout is exploring the urban environment and brings a sequence of 2D images. These images are explained with GPS data and used iteratively as input for a 3D reconstruction engine which reconstructs the 3D models on-the-fly. This turns modeling into an interactive and collaborative task.
Bing Han et. al. presented a different surface fitting approach for 3D dense reconstruction. They proposed a non-linear deterministic annealing algorithm to dissolve the 3D sparse structure to separate regions, and estimate the dense depth map by plane surface fitting. The experimental results reveal that the new approach can segmented in the 3D space geometrically and generates smoother dense depth map.
III. PROPOSED WORK
A. PROBLEM ANALYSIS
Having studied the various previous approaches, techniques and methods used for the recreation of the surface in three dimensions revealed out numbers of issues related to it. The limitations found cannot be eliminated to zero, but can be reduced to an acceptable level by various iterations performed by filtering the point clouds.
Following are the various issues related to it:
1) Computational Time: It is the most important criteria to measure the efficiency of a method. The technique must be time efficient so as to reduce the time spent on the computation of the point clouds and removing unwanted point clouds.
2) Noise: The main factor in all the techniques which should be reduced to minimum is noise. It appears in form of distortion of the original surface. Since accurate model is practically not possible, so an approximate model should be recreated.
3) Space Utilisation: The true requirement is that the surface should utilize less space. Hence, the technique should be chosen such that it minimize the space utilization by removing the unwanted point clouds from the model.
4) Minimum Cost: It always remains the prime factor in every field of technology. High efficiency and low cost is the main criteria to chosose any technique.
Hence, the technique followed must be yield high output at low cost.
B. Problem Statement
Some type of filter technique which can remove insignificant data from original data sets. The researchers are motivated to reduce the cost of surface reconstruction by removing insignificant data, because computation cost is closely related to the complexity of the data. The main aim of the algorithm is to filter out insignificant data while preserving an acceptable level of output quality. In the previous works, reconstruction time and average
distance had been focused. In addition, there are many factors which can be concentrated upon.
C. Proposed work
Power crust algorithm is our proposed work. The hybrid filteration technique is used by the combination of curve filtering and point filtering. Reduction in space points is obtained by using Power crust algorithm. This algorithm gives the better utilization of space. Bad poles are also removed along with the reduction in space. The filteration techniques are also used – curve filtering and point filtering with different values of multiplying factor.
IV. RESULTANDANAYLSIS
Our aim is to reduce the cost of surface reconstruction by applying filtering techniques such as curve filtering and point filtering. Below are shown the results of our proposed work.
1. Here, we first started with a point cloud image which is named as ‗hot dogs‘. Initially the size of the image, without filteration, is 1196826, with multiplying factor, m =1000. Then we applied curve filtering on the original image with different values of curve, C.
Fig 2.. showing original image of hotdog without filteration a) The reduced size is obtained at 0.2 value of C which is 1155676 and this gives reduction in size of approximately 3.4%.
Volume 6, Issue 11, November 2017
Fig. 3 showing hotdog with curve filtering (threshold), C 0.2, giving around 3.4% reduction in
size.
Table for curve filtering applied on Hotdog and corresponding reduction in space.
Fig. 4 graph of space reduction in % vs curve filtering(threshold) for hotdog at various values of curve
filtering.
1. Second iteration we performed on point cloud image
‗knots‘. Without applying filteration, the original size of the image with a multiplying factor m equal to 100, is 369935.
Fig. 5 showing original size of ‗knots‘ without filteration.
a) At C equal to 0.5, the reduced size is 261645, which gives nearly 29% reduction in size.
Fig. 6 representing curve filtering of 0.5 applied on knots.
Table of various values of curve filtering applied on knots and their corresponding %age reduction in
size
Image Name- knot Original Size- 369935
Curve Filtering(Threshold)
Space Reduction in %age
0.3 98
0.4 61
0.5 29
Image Name – hotdogs Original Size- 1196826 Curve Filtering(Threshold) Space Reduction in
%age
0.1 68
0.2 3.4
0.3 0.000083
0.4 0.23
0.5 0.00033
0.6 0.28
0.7 .00027
Fig. 7 Plot between space reduction and curve filtering on ‗knots‘.
The above shown table and graph are for various values curve filtering applied on pts file. There is a considerable decrease in the size by applying filteration. The graph plotted between various values of curve filtering and subsequent decrease in space obtained.
2. Another filtering is performed on point cloud image
‗bunny‘ original size 5313935 at m 1,00,000.
Fig. 8 showing original image of bunny with multiplying factor, m 1,00,000
a) At C 0.1 , the size of image is 3510632 which gives approximately 33% reduction in size.
Fig. 9 curve filtering,C of value 0.1 applied on bunny.
Table for various values of curve filtering applied on ‗bunny‘ and corresponding
reduction in size.
Image Name – Bunny Original Size- 5313935 Curve Filtering(Threshold) Space Reduction in
%age
0.1 33
0.2 8.24
0.3 2.23
0.4 0.96
0.5 0.36
0.6 0.091
Fig. 10 Graph plotted between space reduction and curve filtering (threshold)
Above shown is the table and graphical representation of the curve filteration applied on pts file ,bunny‘. The table shows that there is considerable amount of decrease in space.
Above shown is the table and graphical representation of the curve filteration applied on pts file ,bunny‘. The table shows that there is considerable amount of decrease in space.
Secondly, we will discuss point filtering on point cloud images knots and hotdog.
Volume 6, Issue 11, November 2017 1. Our first concern will be ‗hotdog‘ whose original size
is 672748 with multiplying factor, m 100. Now applying different values of point filtering will yield different results.
Fig. 11 Original image of ‗hotdog‘ without any filteration.
a) With point filtering of 0.7, the size of image obtained is 672487 which gives reduction in size of 0.038%.
Fig. 12 presenting ‗hotdog‘ with point filtering of 0.7 applied on it.
Table of point filtering with different values applied on
‗hotdog‘ giving reduction in size.
Image Name- Hotdog Original size- 672748 Point Filtering
(Threshold)
Space Reduction in %age
0.7 0.038
0.8 0.022
0.9 0.002
Fig. 13 Plot between space reduction and threshold values of point filtering applied on ‗hotdog‘.
Space reduction has been obtained by applying point filtering on pts file named ‗hot dog‘. The Tabular representation as well as graphical representation has been shown above and space reduction is obtained at different values of filtering.
2. Now point filtering is applied on ‗hotdog‘ with combination of curve filtering, keeping value of curve filtering constant and varying the value of point filtering.
Fig. 14 Original image of ‗hot dog‘ without filteration
At first, the value of curve filtering 0.3 is used and value of point filtering is varied.
a) For point filtering 0.5, the reduction in size obtained is 666022 which is 0.99%.
Fig. 15 Curve filtering 0.3 and point filtering 0.5 applied on ‗hotdog‘ giving 0.99% reduction in size.
a) For 0.6 value of point curve, the image of the size 665765 is obtained, around 1.03% reduced size.
Fig. 16 Curve filtering 0.3 and point filtering 0.6 applied on
‗hotdog‘ giving 1.03% reduction in size.
Table Point filtering with different values applied on ‗hotdog‘ giving reduction in size.
Image Name- Hotdog
Original size- 672748 Point Filtering
(Threshold)
Space Reduction in
%age
0.5 0.99
0.6 1.03
0.7 1.02
Fig.17 Plot between space reduction and threshold values of point filtering applied on ‗hotdog‘.
V. CONCLUSION
Here Power Crust algorithm has been implemented with point filtering and curve filtering. Filtering has been applied to calculate the bad poles and remove them. Removing the bad poles from the surface improves the space utilisation and increases efficiency. These points contain important information for surface reconstruction. Less geometric points results in ease of computation hence less computational time.
Geometric patterns become more easier to understand.
VI. FUTURESCOPE
Planned future work includes improving the performance of the algorithm. We have already achieved better reductions in the number of centers but at the cost of slower fitting times.
The main disadvantage is that the image is taken only of pts extension. This is the limitation with the algorithm so we can improve its efficiency by dealing with another image format.
Improvement can also be achieved by reducing the noise that appear in the models so that structure can be more accurately constructed.
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