In this thesis, we propose a new method to improve the visibility of 3D point patterns by enhancing the geometric contrast of faint features. Experimental results show that the proposed method enhances the geometric contrast of 3D point patterns by refining the appearance of weak features. Due to the simplicity of point representation, many researches have been conducted to investigate the applications of 3D point models in various fields.
In this thesis, we improve the visibility of 3D point models by extracting and enhancing the weak features. For a 3D point model, we first detect the weak feature points by using the normal deviation between neighboring points.
Overview of the Proposed Algorithm
Preprocessing
Then we compute a normal vector at each point pi ∈P by analyzing the local neighborhood properties around pi. As seen in Figure 3.3, we estimate the normal vector-→ni atpi by performing PCA (principal component analysis) using the covariance matrix Cofknighboring points ofpi, which is given by. We obtain the pair (Vl, λl), where V is the eigenvector and λ is the eigenvalue, based on equation 3.2.
The normal vector −→ni at the point pi is defined as the eigenvector Vl corresponding to the smallest eigenvalueλl. According to the fundamental eigenanalysis theorem, the eigenpair (Vl, λl) can be found by the following procedure. We then find the eigenvector for a given λl using the Gauss-Jordan elimination method for the set of homogeneous linear equations (C−λlI)Vl = 0.
Since the eigenvalueλl denotes the scale of the corresponding eigenvectorVl, we can considerλlas the variation of neighboring pointsnepi,j according to the direction ofVl. Therefore, when we order the resulting eigenvalues as λ0 ≤ λ1 ≤ λ2, the eigenvector V0 corresponding to the smallest eigenvalue can be considered the normal vector−→niatpi. Then we propagate the normal orientation of−n→afrompato its adjacent point pbal along the most plausible path (Hoppe et al. 1994).
Weak Feature Extraction
First, the normal directions of neighboring points on a smooth surface are almost similar to each other as illustrated in Figure 3.5a. Second, the normal directions of adjacent points on a rough surface are obviously different from each other as shown in Figure 3.5b. However, we introduce the third surface pattern of weak traction, which represents the shallow or slightly protruding patterns as illustrated in Figure 3.5c.
The normal deviationσ(pi)atpi is calculated as the average angle between the two normal vectors of −→ni and −→ni,j, axis. We select pi as a weak feature point, when σ(pi) belongs to a specific user-defined range, which is adaptively set according to a 3D point model. As shown in Figure 3.8a, we can observe some holes and crevices in areas with weak features.
To solve this problem, we replace the holes using a region growing algorithm in the manner of a flood filling algorithm. Then, a weak characteristic point is selected as the starting point, and its neighboring points are checked whether they are weak characteristic points or not, as shown in the figure. If the neighboring points are also weak feature points, they are included in the feature region and serve as the next seed points to grow the region.
Yellow indicates a point belonging to a weak trait, while purple indicates a seed point.
Geometry Histogram Modification
Histogram modification techniques are used to appropriately adjust the contrast of an image by changing the histogram distribution of an image (Gonzalez & Woods 2007). By applying the histogram equalization technique to the image, we make the image histogram more evenly distributed and produce the improved image as shown in Figure 3.10b. The intensity level Ik in the input image is mapped to the intensity level T(Ik) in the resulting image, using equation 3.6.
We first define the geometry histogram for each weak feature region, as illustrated in Figure 3.11. We define the histogram of directional geometry as the probability distribution associated with points in a region with poor features. Therefore, for the same set of points, the geometry histogram gives different distributions according to the choice of the direction vector of the histogram.
We set -→e as the normal vector of the plane that approximates the distribution of p's in a weak traction region and passes through p since p's give the smallest variation in this direction. As shown in Figure 3.12, the original positions of neighboring points are not clearly distinguishable from each other along the direction →e, since the geometry histogram for colors gives a compact distribution within a relatively narrow range of [demin,demax] and thus yields a higher geometry contrast along the histogram direction. Note that no specific range of the is fixed in the geometry histogram, while the range of the intensity values in [0, 255] in the histograms for typical images.
Therefore, a user can adaptively choose the dynamic range of [demin,demax] according to the stretching level of geometry histogram.
Normal Mapping Based Geometry Contrast Enhancement
To mitigate this artifact, we adopt a concept of normal mapping (also known as collision mapping) (Blinn 1978, Cohen et al. 1998). Normal mapping is usually used to create the illusion of detail without adding geometry to 3D models. Such a normal map illusion effect can be performed by superimposing a normal map containing 2D height information on the plain, smooth surface, which ultimately represents the wrinkled surface as illustrated in Figure 3.14.
For example, this spoofing technique is used to improve the appearance and detail of a simple mesh model by producing a normal map from a highly detailed mesh model (Normal Mapping --- Wikipedia, The Free Encyclopedia 2012). It is generally accepted that normal mapping is the same as bump mapping, where bump mapping uses a one-axis normal map, normal mapping utilizes three-axis normal maps that are stored as color images with RGB channels. Motivated by the concept of normal mapping, we introduce a new technique to mitigate the discontinuity artifact.
As shown in Figure 3.15, the estimated normal-→exactly the new position epis was assigned to the corresponding original point p by the mapping function ψ(p).
Fast Processing
Several well-optimized CPU-based KNN algorithms have been presented (Arya et al. 1998) to reduce computation time. Although these are quite competitive, they cannot efficiently handle very large data sets because the distance computation on the general purpose single-core CPU is performed serially. Since the computation of KNN can be parallelizable, we implement this algorithm based on the GPU architecture (Garcia et al. 2008).
To implement the KNN algorithm on the GPUs, we need to build KD trees in the CPU-based system, and then copy the tree information from the host memory to the device memory on the GPUs. As shown in Figure 3.17, a number of basic operations of KNN search can be performed in parallel in GPU architecture. In the middle of the KNN calculation per thread, in particular, we allocate shared memory on the GPUs to store indices and corresponding positions of neighboring points.
We have also used the glDrawArrays API from OpenGL to facilitate simple and fast rendering of points (Wright 2010). For the implementation of the GPU-based KNN algorithm, we have applied the parallel programming procedure to the KD tree construction by using CUDA (Compute Unified Device Architecture) language (Nvidia 2011). In addition, we have also tried to investigate other well-optimized KNN libraries such as FLANN (Fast Library for Approximate Nearest Neighbors) (Muja 2011) and Google's PCL (Point Cloud Library) (Rusu & Cousins 2011), to evaluate our application on GPU - the architecture.
The following table shows the specification of the 3D point models used to evaluate the performance of the proposed method.
Experimental Results
In the thesis, we presented a new concept of geometric contrast and proposed an algorithm for improving the geometric contrast for 3D point models using histogram modification techniques. The geometric histogram for each weak area was defined as the distribution of points along the normal direction to the locally approximated plane. By smoothing and stretching the point distribution, we increased the visibility of the 3D point models and increased the contrast of the geometry.
Furthermore, we presented an alternative rendering method using normal mapping without directly changing the original point positions. The other is that we observe that the unnatural phenomenon cannot be eliminated even if we apply normal mapping-based rendering, since the concept of normal mapping is not sufficient to implement the self-occlusion effect. 1998), Appearance-preserving simplification, in 'Proceedings of the 25th Annual Conference on Computer graphics and Interactive Technics', ACM, pp. 2006), Digital geometry image analysis for medical diagnosis, in 'Proceedings of the 2006 ACM symposium on Applied computing', ACM, pp. 2008), Fast Nearest Neighbor Search Using GPU, in 'Computer Vision and Pattern Recognition Workshops, 2008. IEEE Computer Society Conference on', Ieee, pp. 2007), Digital Image Processing, Prentice Hall . 1994), Surface reconstruction from disorganized points, PhD thesis, University of Washington.
Normal Map --- Wikipedia, The Free Encyclopedia (2012), http://en.wikipedia.org/wiki/. 2011), "Nvidia cuda c programming guide", NVIDIA Corporation. First of all, I would like to express my deep and sincere gratitude to my advisor Prof. I would like to thank my lab colleagues in the Visual Information Processing Lab: Tae-Hui Yun and Su-Yeong Kim, for giving me such a pleasant time while working together for the past year and a half.
Last but not least, I would like to thank my family: my parents Jong-Cheol Nam and Bong-Sun Yang for giving birth to me and supporting me spiritually throughout my life. In addition, I would especially like to thank Chang-Woo Nam, who is my constant mentor as well as my only older brother. Finally, I would like to thank everyone who contributed to the successful completion of this thesis.
