Euclidean distance transformation is a fundamental technique in image understanding and computer vision. Some important characteristics in image analysis such as skeleton and object boundary are based upon the distance transformation computation. In this thesis, we compare our method of computing Euclidean distance transformations with the method of Chamfer distance transformation. Our method is faster and more accurate than the Chamfer method. The boundary detection is an interesting and challenging task in computer vision. We integrate distance transform, watershed transform and active contour model to achieve boundary detection. Our method can successfully separate the touching objects, so as to facilitate the subsequent image processing for obtaining the geometric, and texture characteristics of objects. These features are useful for further medical images applications.

We present a novel framework to exert a topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automated topological changes. In some applications, where some a priori knowledge of the target topology is available, topological changes may not be desirable. A method, based on the concept of simple point borrowed from digital topology, was recently proposed to achieve a strict topology preservation during a level set evolution. However, topologically constrained evolutions often generate topological barriers that lead to large geometric inconsistencies. We introduce a topologically controlled level set framework that greatly alleviates this problem. Unlike existing work, our method allows connected components to merge, split or vanish under some specific conditions that ensure that no topological defects are generated. We demonstrate the strength of our method on a wide range of numerical experiments.

<p>This thesis develops an algorithm for tracking the boundary of an airbag throughout an image sequence. The algorithm is designed to work even if various problematic features, e.g. objects in the background, are present in the image. The work is built on an existing commercially available image processing and analysis suite targeted at the automotive industry. The software suite runs on standard PC hardware. </p><p>Firstly, improvements to the airbag tracking algorithm already available in the suite are considered. Testing reveals that these measures are not sufficient to overcome the problems posed by the problematic image sequences. </p><p>A new tracking algorithmis then proposed. It consists of a Canny edge detector, optional steps to enhance feature detection by removing edges in the background and edges interior to the boundary of the airbag and finally an active contour. The role of the active contour is to produce a closed curve while imposing smoothness constraints on the detected boundary. The active contour is in each frame initialized by linearly extrapolating the contour from previous frames. </p><p>The algorithm works very well and it is fast enough to run on slower machines than was initially targeted.</p>

Image segmentation is an important step in image processing, with many applications such as pattern recognition, object detection, and medical image analysis. It is a technique that separates objects of interests from the background in an image. Geometric active contour is a recent image segmentation method that overcomes previous problems with snakes. It is an attractive method for medical image segmentation as it is able to capture the object of interest in one continuous curve. The theory and implementation details of geometric active contours are discussed in this work. The robustness of the algorithm is tested through a series of tests, involving both synthetic images and medical images. Curve leaking past boundaries is a common problem in cases of non-ideal edges. Noise is also problematic for the advancement of the curve. Smoothing and parameters selection are discussed as ways to help solve these problems. This work also explores the incorporation of the multi-resolution method of Gaussian pyramids into the algorithm. Multi-resolution methods, used extensively in the areas of denoising and edge-selection, can help capture the spatial structure of an image. Results show that similar to the multi-resolution methods applied to parametric active contours, the multi-resolution can greatly increase the computation without sacrificing performance. In fact, results show that with successive smoothing and sub-sampling, performance often improves. Although smoothing and parameter adjustment help improve the performance of geometric active contours, the edge-based approach is still localized and the improvement is limited. Region-based approaches are recommended for further work on active contours.

This thesis develops an algorithm for tracking the boundary of an airbag throughout an image sequence. The algorithm is designed to work even if various problematic features, e.g. objects in the background, are present in the image. The work is built on an existing commercially available image processing and analysis suite targeted at the automotive industry. The software suite runs on standard PC hardware. Firstly, improvements to the airbag tracking algorithm already available in the suite are considered. Testing reveals that these measures are not sufficient to overcome the problems posed by the problematic image sequences. A new tracking algorithmis then proposed. It consists of a Canny edge detector, optional steps to enhance feature detection by removing edges in the background and edges interior to the boundary of the airbag and finally an active contour. The role of the active contour is to produce a closed curve while imposing smoothness constraints on the detected boundary. The active contour is in each frame initialized by linearly extrapolating the contour from previous frames. The algorithm works very well and it is fast enough to run on slower machines than was initially targeted.

Image segmentation is an important step in image processing, with many applications such as pattern recognition, object detection, and medical image analysis. It is a technique that separates objects of interests from the background in an image. Geometric active contour is a recent image segmentation method that overcomes previous problems with snakes. It is an attractive method for medical image segmentation as it is able to capture the object of interest in one continuous curve. The theory and implementation details of geometric active contours are discussed in this work. The robustness of the algorithm is tested through a series of tests, involving both synthetic images and medical images. Curve leaking past boundaries is a common problem in cases of non-ideal edges. Noise is also problematic for the advancement of the curve. Smoothing and parameters selection are discussed as ways to help solve these problems. This work also explores the incorporation of the multi-resolution method of Gaussian pyramids into the algorithm. Multi-resolution methods, used extensively in the areas of denoising and edge-selection, can help capture the spatial structure of an image. Results show that similar to the multi-resolution methods applied to parametric active contours, the multi-resolution can greatly increase the computation without sacrificing performance. In fact, results show that with successive smoothing and sub-sampling, performance often improves. Although smoothing and parameter adjustment help improve the performance of geometric active contours, the edge-based approach is still localized and the improvement is limited. Region-based approaches are recommended for further work on active contours.

The accurate detection of static object boundaries such as contours or surfaces and dynamic tunnels of moving objects via deformable models is an ongoing research topic in computer vision. Most deformable models attempt to converge towards a desired solution by minimizing the sum of internal (prior) and external (measurement) energy terms. Such an approach is elegant, but frequently mis-converges in the presence of noise or complex boundaries and typically requires careful semi-dependent parameter tuning and initialization. Furthermore, current deformable model based approaches are computationally demanding which precludes real-time use. To address these limitations, a decoupled deformable model (DDM) is developed which optimizes the two energy terms separately. Essentially, the DDM consists of a measurement update step, employing a Hidden Markov Model (HMM) and Maximum Likelihood (ML) estimator, followed by a separate prior step, which modifies the updated deformable model based on the relative strengths of the measurement uncertainty and the non-stationary prior. The non-stationary prior is generated by using a curvature guided importance sampling method to capture high curvature regions. By separating the measurement and prior steps, the algorithm is less likely to mis-converge; furthermore, the use of a non-iterative ML estimator allows the method to converge more rapidly than energy-based iterative solvers. The full functionality of the DDM is developed in three phases. First, a DDM in 2D called the decoupled active contour (DAC) is developed to accurately identify the boundary of a 2D object in the presence of noise and background clutter. To carry out this task, the DAC employs the Viterbi algorithm as a truncated ML estimator, curvature guided importance sampling as a non-stationary prior generator, and a linear Bayesian estimator to fuse the non-stationary prior with the measurements. Experimental results clearly demonstrate that the DAC is robust to noise, can capture regions of very high curvature, and exhibits limited dependence on contour initialization or parameter settings. Compared to three other published methods and across many images, the DAC is found to be faster and to offer consistently accurate boundary identification. Second, a fast decoupled active contour (FDAC) is proposed to accelerate the convergence rate and the scalability of the DAC without sacrificing the accuracy by employing computationally efficient and scalable techniques to solve the three primary steps of DAC. The computational advantage of the FDAC is demonstrated both experimentally and analytically compared to three computationally efficient methods using illustrative examples. Finally, an extension of the FDAC from 2D to 3D called a decoupled active surface (DAS) is developed to precisely identify the surface of a volumetric 3D image and the tunnel of a moving 2D object. To achieve the objectives of the DAS, the concepts of the FDAC are extended to 3D by using a specialized 3D deformable model representation scheme and a computationally and storage efficient estimation scheme. The performance of the DAS is demonstrated using several natural and synthetic volumetric images and a sequence of moving objects.

In this dissertation, several GA-based approaches for fractal image compression and active contour model are proposed. The main drawback of the classical fractal image compression is the long encoding time. Two methods are proposed in this dissertation to solve this problem. First, a schema genetic algorithm (SGA), in which the Schema Theorem is embedded in GA, is proposed to reduce the encoding time. In SGA, the genetic operators are adapted according to the Schema Theorem in the evolutionary process performed on the range blocks. We find that such a method can indeed speedup the encoder and also preserve the image quality. Moreover, based on the self-similarity characteristic of the natural image, a spatial correlation genetic algorithm (SC-GA) is proposed to further reduce the encoding time. There are two stages in the SC-GA method. The first stage makes use of spatial correlations in images for both the domain pool and the range pool to exploit local optima. The second stage is operated on the whole image to explore more adequate similarities if the local optima are not satisfactory. Thus not only the encoding speed is accelerated further, but also the higher compression ratio is achieved, because the search space is limited relative to the positions of the previously matched blocks, fewer bits are required to record the offset of the domain block instead of the absolute position. The experimental results of comparing the two methods with the full search, traditional GA, and other GA search methods are provided to demonstrate that they can indeed reduce the encoding time substantially. The main drawback of the traditional active contour model (ACM) for extracting the contour of a given object is that the snake cannot converge to the concave region of the object under consideration. An improved ACM algorithm is proposed in this dissertation to solve this problem. The algorithm is composed of two stages. In the first stage, the ACM with traditional energy function guides the snake to converge to the object boundary except the concave regions. In the second stage, for the control points which stay outside the concave regions, a proper energy template are chosen and are added in the external energy. The modified energy function is applied so as to move the snake toward the concave regions. Therefore, the object of interest can be completely extracted. The experimental results show that, by using this method, the snake can indeed completely extract the boundary of the given object, while the extra cost is very low. In addition, for the problem that the snake cannot precisely extract the object contour when the number of the control points on the snake is not enough, a GA-based ACM algorithm is presented to deal with such a problem. First the improved ACM algorithm is used to guide the snake to approximately extract the object boundary. By utilizing the evolutionary strategy of GA, we attempt to extract precisely the object boundary by adding a few control points into the snake. Similarly, some experimental results are provided to show the performance of the method.

In this dissertation, particle swarm optimization (PSO) is utilized for fractal image compression (FIC) and active contour model (ACM). The dissertation is divided into two parts. The first part is concerned with the FIC and the second part with ACM. FIC is promising both theoretically and practically for image compression. However, since the encoding speed of the traditional full search method is very time-consuming, FIC with full search is unsuitable for real-time applications. In this dissertation, several novel PSO-based approaches incorporating the edge property of the image blocks are proposed to speedup the encoder and preserve the image quality. Instead of the full search, a direction map is built according to the edge type of the image blocks, which directs the particles in the swarm to regions consisting of candidates of higher similarity. Therefore, the searching space is reduced and the speedup can be achieved. Also, since the strategy is performed according to the edge property, better visual effect can be preserved. Experimental results show that the visual-based particle swarm optimization speeds up the encoder 125 times faster with only 0.89 dB decay of image quality in comparison to the full search method. The second part of the dissertation is concerned with the active contour model for automatic object boundary identification. In the traditional methods for ACM, each control point searches its new position in a small nearby window. Consequently, the boundary concavities cannot be searched accurately. Some improvements have been made in the past to enlarge the searching space, yet they are still time-consuming. To overcome these drawbacks, a novel multi-population PSO technique is adopted in this dissertation to enhance the concavity searching capability and reduce the search time but in a larger searching window. In the proposed scheme, to each control point in the contour there is a corresponding swarm of particles with the best swarm particle as the new control point. The proposed optimizer not only inherits the spirit of the original PSO in each swarm but also shares information of the surrounding swarms. Experimental results demonstrate that the proposed method can improve the search of object concavities without extra computation time.

The accurate detection of static object boundaries such as contours or surfaces and dynamic tunnels of moving objects via deformable models is an ongoing research topic in computer vision. Most deformable models attempt to converge towards a desired solution by minimizing the sum of internal (prior) and external (measurement) energy terms. Such an approach is elegant, but frequently mis-converges in the presence of noise or complex boundaries and typically requires careful semi-dependent parameter tuning and initialization. Furthermore, current deformable model based approaches are computationally demanding which precludes real-time use. To address these limitations, a decoupled deformable model (DDM) is developed which optimizes the two energy terms separately. Essentially, the DDM consists of a measurement update step, employing a Hidden Markov Model (HMM) and Maximum Likelihood (ML) estimator, followed by a separate prior step, which modifies the updated deformable model based on the relative strengths of the measurement uncertainty and the non-stationary prior. The non-stationary prior is generated by using a curvature guided importance sampling method to capture high curvature regions. By separating the measurement and prior steps, the algorithm is less likely to mis-converge; furthermore, the use of a non-iterative ML estimator allows the method to converge more rapidly than energy-based iterative solvers. The full functionality of the DDM is developed in three phases. First, a DDM in 2D called the decoupled active contour (DAC) is developed to accurately identify the boundary of a 2D object in the presence of noise and background clutter. To carry out this task, the DAC employs the Viterbi algorithm as a truncated ML estimator, curvature guided importance sampling as a non-stationary prior generator, and a linear Bayesian estimator to fuse the non-stationary prior with the measurements. Experimental results clearly demonstrate that the DAC is robust to noise, can capture regions of very high curvature, and exhibits limited dependence on contour initialization or parameter settings. Compared to three other published methods and across many images, the DAC is found to be faster and to offer consistently accurate boundary identification. Second, a fast decoupled active contour (FDAC) is proposed to accelerate the convergence rate and the scalability of the DAC without sacrificing the accuracy by employing computationally efficient and scalable techniques to solve the three primary steps of DAC. The computational advantage of the FDAC is demonstrated both experimentally and analytically compared to three computationally efficient methods using illustrative examples. Finally, an extension of the FDAC from 2D to 3D called a decoupled active surface (DAS) is developed to precisely identify the surface of a volumetric 3D image and the tunnel of a moving 2D object. To achieve the objectives of the DAS, the concepts of the FDAC are extended to 3D by using a specialized 3D deformable model representation scheme and a computationally and storage efficient estimation scheme. The performance of the DAS is demonstrated using several natural and synthetic volumetric images and a sequence of moving objects.