Bayesian Contour Structure Model And Its Application To Object Segmentation

Analyzing image edges and extracting shape features are both fundamental prob-lems in computer vision area, and have been widely used in various vision tasks suchas shape matching, image segmentation and object recognition and so on. For the edgeanalysis problem, researchers have proposed a lot of effective methods. Among themethods, the Gestalt principles based perceptual edge grouping has recently been thefocus of research. The methods build upon the evidences from the cognition psychol-ogy that the human brain is more sensitive to such salient features as proximity, con-tinuity, parallelism and symmetry, and can group and link the individual image edgesto from boundary. However, the conventional edge grouping method can only capturethe generic salient features without any prior information about the shapes a specificclass of objects. We in this paper go further to study how to incorporate the class spe-cific shape information into the conventional perceptual edge grouping and extend it tothe object segmentation problem that extracts the boundary contours of class specificobjects.Considering the common structure features among the objects of the same class,we propose a robust contour structure model, and characterize in a probabilistic man-ner the confidence that the contour structures form the object boundaries. The model islearned through statistical learning techniques from training samples. To the object seg-mentation problem, we furthermore design a novel energy function which combines thecontour structure model and classic perceptual grouping resulting in a global optimalobject segmentation method. More specifically, our main contributions are:1. We propose a Bayesian Contour Structure Model (BCSM). The BCSM model de-scribes the posterior probability that the sub-structure of edges forms a fragmentof an object boundary given the observed image features. The probabilistic for-mulation is more ?exible and robust than the conventional deterministic structuremode. Also the BCSM model as a local shape model can better handle the objectvariations in shapes, pose and occlusion than the global shape model. To furtherimprove the robustness of the model, we apply the Boosting iterative trainingmethod instead of using the parametric models like Gaussian model to approx-imate the true probability distribution of contour structure. Another advantageof using Boosting method is it can do feature selection of a variety of features such as geometry structure, color and texture. From the training samples, theBCSM model can capture the object related structures rather than the generalsalient features. The experimental results indicate that the proposed model hasgood description ability and robustness to the background clutters and noises.2. We develop an incremental learning scheme to the small size training set. TheBCSM model requires a relatively large set of labeled samples. When the avail-able samples are few there will appear small size training set problem. Directtraining with them may cause the model over-fitting which has low generaliza-tion ability. So that how to utilize the few labeled samples to argument the train-ing set is also what we study here. We first develop a supervised classificationalgorithm based on the minimum incremental coding length theory. The clas-sifier has excellent generalization ability especially in the small sample setting.We apply the classifier the training process of BCSM model where the unlabeledsamples are first classified and then are merged into the training set, thus they areautomatically labeled online.3. Based on the BCSM model, we define a new kind of grouping energy function.The energy function describes the joint posterior probability of object boundary.Assuming the statistical independence among the edge structures, we factorizethe joint probability into a product of probabilities of individual sub-structures.Under the maximum likelihood criterion, searching for the optimal object bound-ary is equal to maximum the joint boundary probability. By taking logarithmoperation, we transfer the maximum likelihood problem to an energy minimumone. Some researches indicate that straightforward optimizing the energy willresult in trivial small cycles known as'small cycle bias'. To reduce the bias, wenormalize the energy with the total length of boundary, and thus we obtain energyin a ratio form of which the numerator describes the likelihood of boundary andthe dominator is the total length. To optimize the normalized energy, we first con-struct a graph with the image edges and perform the ratio cycle algorithm on thegraph. The extracted object boundary is globally optimal since the optimizationis globally optimal. We demonstrate the effectiveness of the proposed methodwith experiments on real data.