Abstract—The goal of this work is to accurately detect and localize boundaries in natural scenes using local image measurements. We formulate features that respond to characteristic changes in brightness, color, and texture associated with natural boundaries. In order to combine the information from these features in an optimal way, we train a classifier using human labeled images as ground truth. The output of this classifier provides the posterior probability of a boundary at each image location and orientation. We present precision-recall curves showing that the resulting detector significantly outperforms existing approaches. Our two main results are 1) that cue combination can be performed adequately with a simple linear model and 2) that a proper, explicit treatment of texture is required to detect boundaries in natural images. Index Terms—Texture, supervised learning, cue combination, natural images, ground truth segmentation data set, boundary detection, boundary localization. 1

This paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture. Natural images contain both textured and untextured regions, so the cues of contour and texture differences are exploited simultaneously. Contours are treated in the intervening contour framework, while texture is analyzed using textons. Each of these cues has a domain of applicability, so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel. Having obtained a local measure of how likely two nearby pixels are to belong to the same region, we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness. Experimental results on a wide range of images are shown.

this paper, we propose a Bayesian theory of hierarchical cortical computation based both on (a) the mathematical and computational ideas of computer vision and pattern the- ory and on (b) recent neurophysiological experimental evidence. We ,2 have proposed that Grenander's pattern theory 3 could potentially model the brain as a generafive model in such a way that feedback serves to disambiguate and 'explain away' the earlier representa- tion. The Helmholtz machine 4, 5 was an excellent step towards approximating this proposal, with feedback implementing priors. Its development, however, was rather limited, dealing only with binary images. Moreover, its feedback mechanisms were engaged only during the learning of the feedforward connections but not during perceptual inference, though the Gibbs sampling process for inference can potentially be interpreted as top-down feedback disambiguating low level representations? Rao and Ballard's predictive coding/Kalman filter model 6 did integrate generafive feedback in the perceptual inference process, but it was primarily a linear model and thus severely limited in practical utility. The data-driven Markov Chain Monte Carlo approach of Zhu and colleagues 7, 8 might be the most successful recent application of this proposal in solving real and difficult computer vision problems using generafive models, though its connection to the visual cortex has not been explored. Here, we bring in a powerful and widely applicable paradigm from artificial intelligence and computer vision to propose some new ideas about the algorithms of visual cortical process- ing and the nature of representations in the visual cortex. We will review some of our and others' neurophysiological experimental data to lend support to these ideas

Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many common computer vision problems naturally map onto the graphical model framework; the representation is a graph where each node contains a portion of the state-space and there is an edge between two nodes only if they are not independent conditional on the other nodes in the graph. When this graph is sparsely connected, belief propagation algorithms can turn an exponential inference computation into one which is linear in the size of the graph. However belief propagation is only applicable when the variables in the nodes are discrete-valued or jointly represented by a single multivariate Gaussian distribution, and this rules out many computer vision applications.

Abstract. We describe a new form of energy functional for the modelling and identification of regions in images. The energy is defined on the space of boundaries in the image domain, and can incorporate very general combinations of modelling information both from the boundary (intensity gradients,...), and from the interior of the region (texture, homogeneity,. We describe two polynomial-time digraph algorithms for finding the global minima of this energy. One of the algorithms is completely general, minimizing the functional for any choice of modelling information. It runs in a few seconds on a 256 × 256 image. The other algorithm applies to a subclass of functionals, but has the advantage of being extremely parallelizable. Neither algorithm requires initialization. 1.

Edge detection is one of the most studied problems in computer vision, yet it remains a very challenging task. It is difficult since often the decision for an edge cannot be made purely based on low level cues such as gradient, instead we need to engage all levels of information, low, middle, and high, in order to decide where to put edges. In this paper we propose a novel supervised learning algorithm for edge and object boundary detection which we refer to as Boosted Edge Learning or BEL for short. A decision of an edge point is made independently at each location in the image; a very large aperture is used providing significant context for each decision. In the learning stage, the algorithm selects and combines a large number of features across different scales in order to learn a discriminative model using an extended version of the Probabilistic Boosting Tree classification algorithm. The learning based framework is highly adaptive and there are no parameters to tune. We show applications for edge detection in a number of specific image domains as well as on natural images. We test on various datasets including the Berkeley dataset and the results obtained are very good. 1.

This paper studies the problem of combining region and boundary cues for natural image segmentation. We employ a large database of manually segmented images in order to learn an optimal affinity function between pairs of pixels. These pairwise affinities can then be used to cluster the pixels into visually coherent groups. Region cues are computed as the similarity in brightness, color, and texture between image patches. Boundary cues are incorporated by looking for the presence of an “intervening contour”, a large gradient along a straight line connecting two pixels. We first use the dataset of human segmentations to individually optimize parameters of the patch and gradient features for brightness, color, and texture cues. We then quantitatively measure the power of different feature combinations by computing the precision and recall of classifiers trained using those features. The mutual information between the output of the classifiers and the same-segment indicator function provides an alternative evaluation technique that yields identical conclusions. As expected, the best classifier makes use of brightness, color, and texture features, in both patch and gradient forms. We find that for brightness, the gradient cue outperforms the patch similarity. In contrast, using color patch similarity yields better results than using color gradients. Texture is the most powerful of the three channels, with both patches and gradients carrying significant independent information. Interestingly, the proximity of the two pixels does not add any information beyond that provided by the similarity cues. We also find that the convexity assumptions made by the intervening contour approach are supported by the ecological statistics of the dataset. 1.

We propose a generic grouping algorithm that constructs a hierarchy of regions from the output of any contour detector. Our method consists of two steps, an Oriented Watershed Transform (OWT) to form initial regions from contours, followed by construction of an Ultrametric Contour Map (UCM) definingahierarchicalsegmentation. We provideextensive experimentalevaluationtodemonstratethat, when coupled to a high-performance contour detector, the OWT-UCM algorithm produces state-of-the-art image segmentations. These hierarchical segmentations can optionally be further refined by user-specified annotations.

Using a saliency measure based on the global property of contour closure, we have developed a segmentation method which identifies smooth closed contours bounding objects of unknown shape in real images. The saliency measure incorporates the Gestalt principles of proximity and good continuity that previous methods have also exploited. Unlike previous methods, we incorporate contour closure by finding the eigenvector with the largest positive real eigenvalue of a transition matrix for aMarkov process whereedges from the image serve as states. Element i; j of the transition matrix is the conditional probability that a contour which contains edge j will also contain edge i. In this paper, we show how the saliency measure, defined for individual edges, can be used to derive a saliency relation, defined for pairs of edges, and further show that strongly-connected components of the graph representing the saliency relation correspond to smooth closed contours in the image. Finally, we report for the first time, results on large real images for which segmentation takes an average of about 10 seconds per object on a general-purpose workstation.

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