2 research outputs found

    Color Image Edge Detection and Segmentation: A Comparison of the Vector Angle and the Euclidean Distance Color Similarity Measures

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    This work is based on Shafer's Dichromatic Reflection Model as applied to color image formation. The color spaces RGB, XYZ, CIELAB, CIELUV, rgb, l1l2l3, and the new h1h2h3 color space are discussed from this perspective. Two color similarity measures are studied: the Euclidean distance and the vector angle. The work in this thesis is motivated from a practical point of view by several shortcomings of current methods. The first problem is the inability of all known methods to properly segment objects from the background without interference from object shadows and highlights. The second shortcoming is the non-examination of the vector angle as a distance measure that is capable of directly evaluating hue similarity without considering intensity especially in RGB. Finally, there is inadequate research on the combination of hue- and intensity-based similarity measures to improve color similarity calculations given the advantages of each color distance measure. These distance measures were used for two image understanding tasks: edge detection, and one strategy for color image segmentation, namely color clustering. Edge detection algorithms using Euclidean distance and vector angle similarity measures as well as their combinations were examined. The list of algorithms is comprised of the modified Roberts operator, the Sobel operator, the Canny operator, the vector gradient operator, and the 3x3 difference vector operator. Pratt's Figure of Merit is used for a quantitative comparison of edge detection results. Color clustering was examined using the k-means (based on the Euclidean distance) and Mixture of Principal Components (based on the vector angle) algorithms. A new quantitative image segmentation evaluation procedure is introduced to assess the performance of both algorithms. Quantitative and qualitative results on many color images (artificial, staged scenes and natural scene images) indicate good edge detection performance using a vector version of the Sobel operator on the h1h2h3 color space. The results using combined hue- and intensity-based difference measures show a slight improvement qualitatively and over using each measure independently in RGB. Quantitative and qualitative results for image segmentation on the same set of images suggest that the best image segmentation results are obtained using the Mixture of Principal Components algorithm on the RGB, XYZ and rgb color spaces. Finally, poor color clustering results in the h1h2h3 color space suggest that some assumptions in deriving a simplified version of the Dichromatic Reflectance Model might have been violated

    Stochastic Nested Aggregation for Images and Random Fields

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    Image segmentation is a critical step in building a computer vision algorithm that is able to distinguish between separate objects in an image scene. Image segmentation is based on two fundamentally intertwined components: pixel comparison and pixel grouping. In the pixel comparison step, pixels are determined to be similar or different from each other. In pixel grouping, those pixels which are similar are grouped together to form meaningful regions which can later be processed. This thesis makes original contributions to both of those areas. First, given a Markov Random Field framework, a Stochastic Nested Aggregation (SNA) framework for pixel and region grouping is presented and thoroughly analyzed using a Potts model. This framework is applicable in general to graph partitioning and discrete estimation problems where pairwise energy models are used. Nested aggregation reduces the computational complexity of stochastic algorithms such as Simulated Annealing to order O(N) while at the same time allowing local deterministic approaches such as Iterated Conditional Modes to escape most local minima in order to become a global deterministic optimization method. SNA is further enhanced by the introduction of a Graduated Models strategy which allows an optimization algorithm to converge to the model via several intermediary models. A well-known special case of Graduated Models is the Highest Confidence First algorithm which merges pixels or regions that give the highest global energy decrease. Finally, SNA allows us to use different models at different levels of coarseness. For coarser levels, a mean-based Potts model is introduced in order to compute region-to-region gradients based on the region mean and not edge gradients. Second, we develop a probabilistic framework based on hypothesis testing in order to achieve color constancy in image segmentation. We develop three new shading invariant semi-metrics based on the Dichromatic Reflection Model. An RGB image is transformed into an R'G'B' highlight invariant space to remove any highlight components, and only the component representing color hue is preserved to remove shading effects. This transformation is applied successfully to one of the proposed distance measures. The probabilistic semi-metrics show similar performance to vector angle on images without saturated highlight pixels; however, for saturated regions, as well as very low intensity pixels, the probabilistic distance measures outperform vector angle. Third, for interferometric Synthetic Aperture Radar image processing we apply the Potts model using SNA to the phase unwrapping problem. We devise a new distance measure for identifying phase discontinuities based on the minimum coherence of two adjacent pixels and their phase difference. As a comparison we use the probabilistic cost function of Carballo as a distance measure for our experiments
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