Joseph L. Mundy

Invariant descriptors for 3D object recognition and pose

Invariant descriptors are shape descriptors that are unaffected by object pose, by perspective projection, or by the intrinsic parameters of the camera. These descriptors can be constructed using the methods of invariant theory, which are briefly surveyed. A range of applications of invariant descriptors in 3D model-based vision is demonstrated. First, a model-based vision system that recognizes curved plane objects irrespective of their pose is demonstrated. Curves are not reduced to polyhedral approximations but are handled as objects in their own right. Models are generated directly from image data. Once objects have been recognized, their pose can be computed. Invariant descriptors for 3D objects with plane faces are described. All these ideas are demonstrated using images of real scenes. The stability of a range of invariant descriptors to measurement error is treated in detail. >

Three-dimensional model matching from an unconstrained viewpoint

It is demonstrated that the affine viewing transformation is a reasonable approximation to perspective. A group of image vertices and edges, called the vertex-pair, which fully determines the affine transformation between a three-dimensional model and a two-dimensional image is defined. A clustering approach, which produces a set of consistent assignments between vertex-pairs in the model and in the image is described. A number of experimental results on outdoor images are presented.

Planar object recognition using projective shape representation

We describe a model based recognition system, called LEWIS, for the identification of planar objects based on a projectively invariant representation of shape. The advantages of this shape description include simple model acquisition (direct from images), no need for camera calibration or object pose computation, and the use of index functions. We describe the feature construction and recognition algorithms in detail and provide an analysis of the combinatorial advantages of using index functions. Index functions are used to select models from a model base and are constructed from projective invariants based on algebraic curves and a canonical projective coordinate frame. Examples are given of object recognition from images of real scenes, with extensive object libraries. Successful recognition is demonstrated despite partial occlusion by unmodelled objects, and realistic lighting conditions.

Extracting projective structure from single perspective views of 3D point sets

A number of recent papers have argued that invariants do not exist for three-dimensional point sets in general position, which has often been misinterpreted to mean that invariants cannot be computed for any three-dimensional structure. It is proved by example that although the general statement is true, invariants do exist for structured three-dimensional point sets. Projective invariants are derived for two object classes: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: they can be used for recognition, and they can be used to compute projective structure. Examples of invariants computed from real images are given.<<ETX>>

Canonical Frames for Planar Object Recognition

We present a canonical frame construction for determining projectively invariant indexing functions for non-algebraic smooth plane curves. These invariants are semi-local rather than global, which promotes tolerance to occlusion.

3D object recognition using invariance

Abstract The systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years. Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpoint. This problem is entirely avoided if the geometric description is unaffected by the imaging transformation. Such invariant descriptions can be measured from images without any prior knowledge of the position, orientation and calibration of the camera. These invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification. Object models can be acquired directly from images, allowing efficient construction of model libraries without manual intervention. A significant part of the paper is a summary of recent results on the construction of invariants for 3D objects from a single perspective view. A proposed recognition architecture is described which enables the integration of multiple general object classes and provides a means for enforcing global scene consistency. Various criticisms of the invariant approach are articulated and addressed.

Driving vision by topology

Recently, vision research has centred on the extraction and organization of geometric features, and on geometric relations. It is largely assumed that topological structure, that is linked edgel chains and junctions, cannot be extracted reliably from image intensity data. In this paper we demonstrate that this view is overly pessimistic and that visual tasks, such as perceptual grouping, can be carried out much more efficiently and reliably if well-formed topological structures are available. Towards this end, we describe an edge detection algorithm designed to recover much better scene topology than previously considered possible. In doing this we need make no sacrifice to geometric accuracy of the edge description.

A Probabilistic-Based Design Methodology for Nanoscale Computation

As current silicon-based techniques fast approach their practicallimits, the investigation of nanoscale electronics, devices andsystem architectures becomes a central research priority. It is expectedthat nanoarchitectures will confront devices and interconnectionswith high inherent defect rates, which motivates the searchfor new architectural paradigms.In this paper, we propose a probabilistic-based design methodologyfor designing nanoscale computer architectures based onMarkov Random Fields (MRF). The MRF can express arbitrarylogic circuits and logic operation is achieved by maximizing theprobability of state configurations in the logic network. Maximizingstate probability is equivalent to minimizing a form of energythat depends on neighboring nodes in the network. Once we developa library of elementary logic components, we can link themtogether to build desired architectures based on the belief propagationalgorithm. Belief propagation is a way of organizing theglobal computation of marginal belief in terms of smaller localcomputations. We will illustrate the proposed design methodologywith some elementary logic examples.

Designing logic circuits for probabilistic computation in the presence of noise

As Si CMOS devices are scaled down into the nanoscale regime, current computer architecture approaches are reaching their practical limits. Future nano-architectures confront devices and interconnections with a large number of inherent defects, which motivates the search for new architectural paradigms. In this paper, we examine probabilistic-based design methodologies for nanoscale computer architectures based on Markov random fields (MRF). The MRF approach can express arbitrary logic circuits and the logic operation is achieved by maximizing the probability of correct state configurations in the logic network depending on the interaction of neighboring circuit nodes. The computation proceeds via probabilistic propagation of states through the circuit. Crucially, the MRF logic can be implemented in modified CMOS-based circuitry that trades off circuit area and operation speed for the crucial fault tolerance and noise immunity. This paper builds on the recent demonstration that significant immunity to faulty individual devices or dynamically occurring signal errors can be achieved by the propagation of state probabilities over an MRF network. In particular, we are interested in CMOS-based circuits that work reliably at very low supply voltages (V/sup DD/ = 0.1-0.2 V), where standard CMOS would fail due to thermal and crosstalk noise, and transistor threshold variation. In this paper, we present results for simulated probabilistic test circuits for elementary logic components and well as small circuits taken from the MCNC91 benchmark suite and we show greatly improved noise immunity operating at very low V/sup DD/. The MRF framework extends to all levels of a design, where formally optimum probabilistic computation can be implemented as a natural element of the processing structure.

Object Recognition in the Geometric Era: A Retrospective

Recent advances in object recognition have emphasized the integration of intensity-derived features such as affine patches with associated geometric constraints leading to impressive performance in complex scenes. Over the four previous decades, the central paradigm of recognition was based on formal geometric object descriptions with a focus on the properties of such descriptions under perspective image formation. This paper will review the key advances of the geometric era and investigate the underlying causes of the movement away from formal geometry and prior models towards the use of statistical learning methods based on appearance features.