. A variety of computer vision problems can be optimally posed as Bayesian labeling in which the solution of a problem is defined as the maximum a posteriori (MAP) probability estimate of the true labeling. The posterior probability is usually derived from a prior model and a likelihood model. The latter relates to how data is observed and is problem domain dependent. The former depends on how various prior constraints are expressed. Markov Random Field Models (MRF) theory is a tool to encode contextual constraints into the prior probability. This paper presents a unified approach for MRF modeling in low and high level computer vision. The unification is made possible due to a recent advance in MRF modeling for high level object recognition. Such unification provides a systematic approach for vision modeling based on sound mathematical principles. 1 Introduction Since its beginning in early 1960's, computer vision research has been evolving from heuristic design of algorithms to syste...

Most artificial intelligence systems today work on simple problems and artificial domains because they rely on the accurate sensing of the task world. Object recognition is a crucial part of the sensing challenge and machine learning stands in a position to catapult object recognition into real world domains. Given that, to date, machine learning has not delivered general object recognition, we propose a different point of attack: the learning architectures themselves. We have developed a method for directly learning and combining algorithms in a new way that imposes little burden on or bias from the humans involved. This learning architecture, PADO, and the new results it brings to the problem of natural image object recognition is the focus of this chapter.

A variety of analytic and probabilistic models in connection to Markov random fields (MRFs) have been proposed in the last decade for solving low level vision problems involving discontinuities. This paper presents a systematic study on these models and defines a general discontinuity adaptive (DA) MRF model. By analyzing the Euler equation associated with the energy minimization, it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points, which is determined by the a priori smoothness constraint encoded into the energy function An important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing. This forms the basis on which a class of adaptive interaction functions (AIFs) is defined. The DA model is defined in terms of the Euler equation constrained by this class of AIFs. Its solution is C 1 continuous and allows arbitrarily large but bounded slopes in dealing...

Most artificial intelligence systems today work on simple problems and artificial domains because they rely on the accurate sensing of the task world. Object recognition is a crucial part of the sensing challenge and machine learning stands in a position to catapult object recognition into real world domains. Given that, to date, machine learning has not delivered general object recognition, we propose a different point of attack: the learning architectures themselves. We have developed a method for directly learning and combining algorithms in a new way that imposes little burden on or bias from the humans involved. This learning architecture, PADO, and the new results it brings to the problem of natural image object recognition is the focus of this report. 1 This research was sponsored by the Carnegie Mellon School of Computer Science Keywords: PADO, Genetic Programming, Object Recognition, Evolution,Parallel Algorithms,Incremental Learning,Natural Images,Greyscale Video Images,Li...

A locally excitatory globally inhibitory oscillator network (LEGION) is constructed and applied to range image segmentation, where each oscillator has excitatory lateral connections to the oscillators in its local neighborhood as well as a connection with a global inhibitor. A feature vector, consisting of depth, surface normal, and mean and Gaussian curvatures, is associated with each oscillator and is estimated from local windows at its corresponding pixel location. A context-sensitive method is applied in order to obtain more reliable and accurate estimations. The lateral connection between two oscillators is established based on a similarity measure of their feature vectors. The emergent behavior of the LEGION network gives rise to segmentation. Due to the flexible representation through phases, our method needs no assumption about the underlying structures in image data and no prior knowledge regarding the number of regions. More importantly, the network is guaranteed to converge rapidly under general conditions. These unique properties may lead to a real-time approach for range image segmentation in machine perception.

. An invariant representation based on so-called similarity-invariant coordinate system (SICS) is presented for matching 3D space curves under the group of similarity transformations. In the SICS, the 3D geometry of a curve segment is unique. Thus, constraints on the curve can be fully explored for the matching. Experimental results with simulated data are presented. 1 Introduction Object recognition is an important problem in computer vision [1]. One of the approaches to solving it is through matching characteristic curves on objects. Although much work is done on representation and matching of 2D planar curves, less is seen for 3D space curves [2, 3, 12], especially non-algebraic curves, and even less has been reported for the situation where the scale of objects in 3D is an unknown factor. A frequently cited paper on 3D curve matching is [12]. There, the group of transformations dealt with is Euclidean, in which the scale is known; and connected curves are assumed to have been segm...

Discontinuity adaptive MRF priors have been used for modeling vision problems involving discontinuities and robust statistics models for solving regression problems involving outliers. This paper presents a comparative study of the two kinds of models. We analyze the mechanisms of adaptation (to discontinuities) and robustness (to outliers) and give a necessary condition for the adaptation and the robustness. We then give a common definition of both models. The definition captures the essence of the adaptation ability and gives in theory infinitely many choices of functions suitable for the adaptation in MRF and robust models. The likeness between the two models suggests that results in the two areas are interchangeable to benefit each other. Index terms --- Discontinuities, Markov random fields, robust statistics. Introduction Markov random field (MRF) theory provides a theoretic basis for modeling joint prior probabilities to prior contextual constraints by specifying appropriate ...

this article are addressed mainly from the computational viewpoint. The primary concerns are how to dene an objective function for the optimal solution for an image analysis problem and how to nd the optimal solution. The reason for dening the solution in an optimization sense is due to various uncertainties in imaging processes. It may be dicult to nd the perfect solution, so we usually look for an optimal one in the sense that an objective, into which constraints are encoded, is optimized

This paper presents a system for matching and pose estimation of 3D space curves under the similarity transformation composed of rotation, translation and uniform scaling. The system makes use of constraints not only on the feature points but also on the curve segment. A representation called the similarity-invariant coordinate system (SICS) is presented for deriving semi-local invariants of 3D curves. The SICS also enables an efficient exploration of constraints on the shape of the entire curve. Model-based curve matching is performed in the principle of maximum

A Bayesian approach for object matching is presented. An object and a scene are each represented by its features, such as critical points, line segments and surface patches, constrained by unary properties and contextual relations. The matching is posed as a labeling problem where each feature in the scene is assigned (associated with) a feature of the known model objects. The prior distribution of a scene labeling is modeled as a Markov random field (MRF), which encodes the between-object constraints. The conditional distribution of the observed features given the labeling is assumed to be Gaussian, which encodes the within-object constraints. An optimal solution is defined as a maximum a posteriori (MAP) estimate. Relationships with previous work are discussed. Experimental results are shown. 1 Introduction Object matching and recognition is a high level vision task. For non-simple objects, it is usually performed on object features, such as critical points, line segments and surfac...