Exploiting sparsity and sharing in probabilistic sensor data models

Probabilistic sensor models defined as dynamic Bayesian networks can possess an inherent sparsity that is not reflected in the structure of the network. Classical inference algorithms like variable elimination and junction tree propagation cannot exploit this sparsity. Also, they do not exploit the opportunities for sharing calculations among different time slices of the model. We show that, using a relational representation, inference expressions for these sensor models can be rewritten to make efficient use of sparsity and sharing

Computational models for image contour grouping

Contours are one dimensional curves which may correspond to meaningful entities such as object boundaries. Accurate contour detection will simplify many vision tasks such as object detection and image recognition. Due to the large variety of image content and contour topology, contours are often detected as edge fragments at first, followed by a second step known as {u0300}{u0300}contour grouping'' to connect them. Due to ambiguities in local image patches, contour grouping is essential for constructing globally coherent contour representation. This thesis aims to group contours so that they are consistent with human perception. We draw inspirations from Gestalt principles, which describe perceptual grouping ability of human vision system. In particular, our work is most relevant to the principles of closure, similarity, and past experiences. The first part of our contribution is a new computational model for contour closure. Most of existing contour grouping methods have focused on pixel-wise detection accuracy and ignored the psychological evidences for topological correctness. This chapter proposes a higher-order CRF model to achieve contour closure in the contour domain. We also propose an efficient inference method which is guaranteed to find integer solutions. Tested on the BSDS benchmark, our method achieves a superior contour grouping performance, comparable precision-recall curves, and more visually pleasant results. Our work makes progresses towards a better computational model of human perceptual grouping. The second part is an energy minimization framework for salient contour detection problem. Region cues such as color/texture homogeneity, and contour cues such as local contrast, are both useful for this task. In order to capture both kinds of cues in a joint energy function, topological consistency between both region and contour labels must be satisfied. Our technique makes use of the topological concept of winding numbers. By using a fast method for winding number computation, we find that a small number of linear constraints are sufficient for label consistency. Our method is instantiated by ratio-based energy functions. Due to cue integration, our method obtains improved results. User interaction can also be incorporated to further improve the results. The third part of our contribution is an efficient category-level image contour detector. The objective is to detect contours which most likely belong to a prescribed category. Our method, which is based on three levels of shape representation and non-parametric Bayesian learning, shows flexibility in learning from either human labeled edge images or unlabelled raw images. In both cases, our experiments obtain better contour detection results than competing methods. In addition, our training process is robust even with a considerable size of training samples. In contrast, state-of-the-art methods require more training samples, and often human interventions are required for new category training. Last but not least, in Chapter 7 we also show how to leverage contour information for symmetry detection. Our method is simple yet effective for detecting the symmetric axes of bilaterally symmetric objects in unsegmented natural scene images. Compared with methods based on feature points, our model can often produce better results for the images containing limited texture

Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts

Formulations of the Image Decomposition Problem as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with long-range terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark. The decompositions we obtain do not differ significantly from the state of the art, suggesting that the LMP is a competitive formulation of the Image Decomposition Problem. To demonstrate the generality of the LMP, we apply it also to the Mesh Decomposition Problem posed by the Princeton benchmark, obtaining state-of-the-art decompositions

A Stochastic Grammar of Images

This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and non-terminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple And-Or graph representation where each Or-node points to alternative sub-configurations and an And-node is decomposed into a number of components. This representation supports recursive top-down/bottom-up procedures for image parsing under the Bayesian framework and make it convenient to scale up in complexity. Given an input image, the image parsing task constructs a most probable parse graph on-the-fly as the output interpretation and this parse graph is a subgraph of the And-Or graph after making choice on the Or-nodes. (iii) A probabilistic model is defined on this And-Or graph representation to account for the natural occurrence frequency of objects and parts as well as their relations. This model is learned from a relatively small training set per category and then sampled to synthesize a large number of configurations to cover novel object instances in the test set. This generalization capability is mostly missing in discriminative machine learning methods and can largely improve recognition performance in experiments. (iv) To fill the well-known semantic gap between symbols and raw signals, the grammar includes a series of visual dictionaries and organizes them through graph composition. At the bottom-level the dictionary is a set of image primitives each having a number of anchor points with open bonds to link with other primitives. These primitives can be combined to form larger and larger graph structures for parts and objects. The ambiguities in inferring local primitives shall be resolved through top-down computation using larger structures. Finally these primitives forms a primal sketch representation which will generate the input image with every pixels explained. The proposal grammar integrates three prominent representations in the literature: stochastic grammars for composition, Markov (or graphical) models for contexts, and sparse coding with primitives (wavelets). It also combines the structure-based and appearance based methods in the vision literature. Finally the paper presents three case studies to illustrate the proposed grammar.Mathematic

Maximum Entropy Discrimination

We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric class, in the context of anomaly detection rather than classification, or when the labels in the training set are uncertain or incomplete. Support vector machines are naturally subsumed under this class and we provide several extensions. We are also able to estimate exactly and efficiently discriminative distributions over tree structures of class-conditional models within this framework. Preliminary experimental results are indicative of the potential in these techniques

A new straight line reconstruction methodology from multi-spectral stereo aerial images

In this study, a new methodology for the reconstruction of line features from multispectral stereo aerial images is presented. We take full advantage of the existing multispectral information in aerial images all over the steps of pre-processing and edge detection. To accurately describe the straight line segments, a principal component analysis technique is adapted. The line to line correspondences between the stereo images are established using a new pair-wise stereo matching approach. The approach involves new constraints, and the redundancy inherent in pair relations gives us a possibility to reduce the number of false matches in a probabilistic manner. The methodology is tested over three different urban test sites and provided good results for line matching and reconstruction