Surface Reconstruction from Multiple Views using Rational B-Splines and Knot Insertion

A method for reconstruction of 3D rational B-spline surfaces from multiple views is proposed. Given corresponding features in multiple views, though not necessarily visible in all views, the surface is reconstructed. First 2D B-spline patches are fitted to each view. The 3D B-splines and projection matricies can then be extracted from the 2D B-splines using factorization methods. The surface fit is then further refined via an iterative procedure. Finally, a hierarchal fitting scheme is proposed to allow modeling of complex surfaces by means of knot insertion. Experiments with real imagery demonstrate the efficacy of the approach.

Surface Reconstruction from Multiple Views using Rational B-Splines

A method for reconstructing 3D rational B-spline surfaces from multiple views is proposed. The method takes advantage of the projective invariance properties of rational B-splines. Given feature correspondences in multiple views, the 3D surface is reconstructed via a four step framework. First, corresponding features in each view are given an initial surface parameter value (s; t), and a 2D B-spline is fitted in each view. After this initialization, an iterative minimization procedure alternates between updating the 2D B-spline control points and re-estimating each feature's (s; t). Next, a non-linear minimization method is used to upgrade the 2D B-splines to 2D rational B-splines, and obtain a better fit. Finally, a factorization method is used to reconstruct the 3D B-spline surface given 2D B-splines in each view. This surface recovery method can be applied in both the perspective and orthographic case. The orthographic case allows the use of additional constraints in the recovery. Experiments with real and synthetic imagery demonstrate the efficacy of the approach for the orthographic case.

Tracking a Large Number of Objects from Multiple Views

We propose a multi-object multi-camera framework for tracking large numbers of tightly-spaced objects that rapidly move in three dimensions. We formulate the problem of finding correspondences across multiple views as a multidimensional assignment problem and use a greedy randomized adaptive search procedure to solve this NP-hard problem efficiently. To account for occlusions, we relax the one-to-one constraint that one measurement corresponds to one object and iteratively solve the relaxed assignment problem. After correspondences are established, object trajectories are estimated by stereoscopic reconstruction using an epipolar-neighborhood search. We embedded our method into a tracker-to-tracker multi-view fusion system that not only obtains the three-dimensional trajectories of closely-moving objects but also accurately settles track uncertainties that could not be resolved from single views due to occlusion. We conducted experiments to validate our greedy assignment procedure and our technique to recover from occlusions. We successfully track hundreds of flying bats and provide an analysis of their group behavior based on 150 reconstructed 3D trajectories.

Stochastic Refinement of the Visual Hull to Satisfy Photometric and Silhouette Consistency Constraints

An iterative method for reconstructing a 3D polygonal mesh and color texture map from multiple views of an object is presented. In each iteration, the method first estimates a texture map given the current shape estimate. The texture map and its associated residual error image are obtained via maximum a posteriori estimation and reprojection of the multiple views into texture space. Next, the surface shape is adjusted to minimize residual error in texture space. The surface is deformed towards a photometrically-consistent solution via a series of 1D epipolar searches at randomly selected surface points. The texture space formulation has improved computational complexity over standard image-based error approaches, and allows computation of the reprojection error and uncertainty for any point on the surface. Moreover, shape adjustments can be constrained such that the recovered model's silhouette matches those of the input images. Experiments with real world imagery demonstrate the validity of the approach.

A Neural Network of Adaptively Timed Reinforcement Learning and Hippocampal Dynamics

A neural model is described of how adaptively timed reinforcement learning occurs. The adaptive timing circuit is suggested to exist in the hippocampus, and to involve convergence of dentate granule cells on CA3 pyramidal cells, and NMDA receptors. This circuit forms part of a model neural system for the coordinated control of recognition learning, reinforcement learning, and motor learning, whose properties clarify how an animal can learn to acquire a delayed reward. Behavioral and neural data are summarized in support of each processing stage of the system. The relevant anatomical sites are in thalamus, neocortex, hippocampus, hypothalamus, amygdala, and cerebellum. Cerebellar influences on motor learning are distinguished from hippocampal influences on adaptive timing of reinforcement learning. The model simulates how damage to the hippocampal formation disrupts adaptive timing, eliminates attentional blocking, and causes symptoms of medial temporal amnesia. It suggests how normal acquisition of subcortical emotional conditioning can occur after cortical ablation, even though extinction of emotional conditioning is retarded by cortical ablation. The model simulates how increasing the duration of an unconditioned stimulus increases the amplitude of emotional conditioning, but does not change adaptive timing; and how an increase in the intensity of a conditioned stimulus "speeds up the clock", but an increase in the intensity of an unconditioned stimulus does not. Computer simulations of the model fit parametric conditioning data, including a Weber law property and an inverted U property. Both primary and secondary adaptively timed conditioning are simulated, as are data concerning conditioning using multiple interstimulus intervals (ISIs), gradually or abruptly changing ISis, partial reinforcement, and multiple stimuli that lead to time-averaging of responses. Neurobiologically testable predictions are made to facilitate further tests of the model.

Stochastic Mesh-Based Multiview Reconstruction

A method for reconstruction of 3D polygonal models from multiple views is presented. The method uses sampling techniques to construct a texture-mapped semi-regular polygonal mesh of the object in question. Given a set of views and segmentation of the object in each view, constructive solid geometry is used to build a visual hull from silhouette prisms. The resulting polygonal mesh is simplified and subdivided to produce a semi-regular mesh. Regions of model fit inaccuracy are found by projecting the reference images onto the mesh from different views. The resulting error images for each view are used to compute a probability density function, and several points are sampled from it. Along the epipolar lines corresponding to these sampled points, photometric consistency is evaluated. The mesh surface is then pulled towards the regions of higher photometric consistency using free-form deformations. This sampling-based approach produces a photometrically consistent solution in much less time than possible with previous multi-view algorithms given arbitrary camera placement.