A Lower-Bound Result on the Power of a Genetic Algorithm

This paper presents a lower-bound result on the computational power of a genetic algorithm in the context of combinatorial optimization. We describe a new genetic algorithm, the merged genetic algorithm, and prove that for the class of monotonic functions, the algorithm finds the optimal solution, and does so with an exponential convergence rate. The analysis pertains to the ideal behavior of the algorithm where the main task reduces to showing convergence of probability distributions over the search space of combinatorial structures to the optimal one. We take exponential convergence to be indicative of efficient solvability for the sample-bounded algorithm, although a sampling theory is needed to better relate the limit behavior to actual behavior. The paper concludes with a discussion of some immediate problems that lie ahead.

Contour Generator Points for Threshold Selection and a Novel Photo-Consistency Measure for Space Carving

Space carving has emerged as a powerful method for multiview scene reconstruction. Although a wide variety of methods have been proposed, the quality of the reconstruction remains highly-dependent on the photometric consistency measure, and the threshold used to carve away voxels. In this paper, we present a novel photo-consistency measure that is motivated by a multiset variant of the chamfer distance. The new measure is robust to high amounts of within-view color variance and also takes into account the projection angles of back-projected pixels. Another critical issue in space carving is the selection of the photo-consistency threshold used to determine what surface voxels are kept or carved away. In this paper, a reliable threshold selection technique is proposed that examines the photo-consistency values at contour generator points. Contour generators are points that lie on both the surface of the object and the visual hull. To determine the threshold, a percentile ranking of the photo-consistency values of these generator points is used. This improved technique is applicable to a wide variety of photo-consistency measures, including the new measure presented in this paper. Also presented in this paper is a method to choose between photo-consistency measures, and voxel array resolutions prior to carving using receiver operating characteristic (ROC) curves.

On trip planning queries in spatial databases

In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks.

Combinations of Deformable Shape Prototypes

We propose to investigate a model-based technique for encoding non-rigid object classes in terms of object prototypes. Objects from the same class can be parameterized by identifying shape and appearance invariants of the class to devise low-level representations. The approach presented here creates a flexible model for an object class from a set of prototypes. This model is then used to estimate the parameters of low-level representation of novel objects as combinations of the prototype parameters. Variations in the object shape are modeled as non-rigid deformations. Appearance variations are modeled as intensity variations. In the training phase, the system is presented with several example prototype images. These prototype images are registered to a reference image by a finite element-based technique called Active Blobs. The deformations of the finite element model to register a prototype image with the reference image provide the shape description or shape vector for the prototype. The shape vector for each prototype, is then used to warp the prototype image onto the reference image and obtain the corresponding texture vector. The prototype texture vectors, being warped onto the same reference image have a pixel by pixel correspondence with each other and hence are "shape normalized". Given sufficient number of prototypes that exhibit appropriate in-class variations, the shape and the texture vectors define a linear prototype subspace that spans the object class. Each prototype is a vector in this subspace. The matching phase involves the estimation of a set of combination parameters for synthesis of the novel object by combining the prototype shape and texture vectors. The strengths of this technique lie in the combined estimation of both shape and appearance parameters. This is in contrast with the previous approaches where shape and appearance parameters were estimated separately.

Recursive Estimation of Motion and Planar Structure

A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the number of feature points needed to estimate the state. Experiments with synthetic data and real imagery illustrate the system performance. The experiments confirm that the specialized formulation provides improved accuracy, stability to observation noise, and rate of convergence in estimation for the case where the tracked points lie on a plane.

An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.

A Neural Theory of Attentive Visual Search: Interactions of Boundary, Surface, Spatial, and Object Representations

Visual search data are given a unified quantitative explanation by a model of how spatial maps in the parietal cortex and object recognition categories in the inferotemporal cortex deploy attentional resources as they reciprocally interact with visual representations in the prestriate cortex. The model visual representations arc organized into multiple boundary and surface representations. Visual search in the model is initiated by organizing multiple items that lie within a given boundary or surface representation into a candidate search grouping. These items arc compared with object recognition categories to test for matches or mismatches. Mismatches can trigger deeper searches and recursive selection of new groupings until a target object io identified. This search model is algorithmically specified to quantitatively simulate search data using a single set of parameters, as well as to qualitatively explain a still larger data base, including data of Aks and Enns (1992), Bravo and Blake (1990), Chellazzi, Miller, Duncan, and Desimone (1993), Egeth, Viri, and Garbart (1984), Cohen and Ivry (1991), Enno and Rensink (1990), He and Nakayarna (1992), Humphreys, Quinlan, and Riddoch (1989), Mordkoff, Yantis, and Egeth (1990), Nakayama and Silverman (1986), Treisman and Gelade (1980), Treisman and Sato (1990), Wolfe, Cave, and Franzel (1989), and Wolfe and Friedman-Hill (1992). The model hereby provides an alternative to recent variations on the Feature Integration and Guided Search models, and grounds the analysis of visual search in neural models of preattentive vision, attentive object learning and categorization, and attentive spatial localization and orientation.