The pinhole camera in single photon emission computed tomography (SPECT) has an inherent trade-off between resolution and sensitivity. Recent systems overcome this to some extent by utilizing multiple pinholes distributed around the imaging object. The present work is a theoretical study on how to optimally construct such systems. We use an analytic model to analyze the multipinhole SPECT geometry and identify the underlying trade-offs. One of the results is the derivation of the upper bound for the sensitivity, given the geometric resolution and field-of-view (FOV). Reaching this bound requires an infinitely large detector. However, a sensitivity very close to the upper bound can be achieved by a system with realistic proportions. We show that it is usually possible to get a sensitivity that is 95%-99% of the upper bound. Further analysis reveals a trade-off between sensitivity, magnification, and the number of pinholes. Based on this new theory, we develop a strategy for multipinhole SPECT design, from which a number of example systems are computed. Penetration in the pinhole knife edge is accounted for by using the resolution and sensitivity equivalent apertures.

Many objects have smooth surfaces of a fairly uniform color, thereby exhibiting shading patterns that reveal information about its shape, an important clue to the nature of the object. This papers explores extracting this information from images, by creating shape detectors based on shading.

Multi-target tracking requires locating the targets and labeling their identities. The latter is a challenge when many targets, with indistinct appearances, frequently occlude one another, as in football and surveillance tracking. We present an approach to solving this labeling problem. When isolated, a target can be tracked and its identity maintained. While, if targets interact this is not always the case. This paper assumes a track graph exists, denoting when targets are isolated and describing how they interact. Measures of similarity between isolated tracks are defined. The goal is to associate the identities of the isolated tracks, by exploiting the graph constraints and similarity measures. We formulate this as a Bayesian network inference problem, allowing us to use standard message propagation to find the most probable set of paths in an efficient way. The high complexity inevitable in large problems is gracefully reduced by removing dependency links between tracks. We apply the method to a 10 min sequence of an international football game and compare results to ground truth.

The aim of this paper is to find the best representation for the appearance of surfaces with Lambertian reflectance under varying illumination. Previous work using principal component analysis (PCA) found the best sub-space to represent all images of an object under a varying point light source. We extend this to images from any illumination distribution. Specifically we calculate the bases for all configurations of a point plus ambient light source and two point light sources, as well as from a database of captured real world illumination. We also reformulate the optimization criterion used in PCA. The resulting basis, we believe has higher representability and is better for analyzing images of shaded objects. The different bases are compared on a database of images to test the representability.

We present a framework for calculating low-dimensional bases to represent image irradiance from surfaces with isotropic reflectance under arbitrary illumination. By representing the illumination and the bidirectional reflectance distribution function (BRDF) in frequency space, a model for the image irradiance is derived. This model is then reduced in dimensionality by analytically constructing the principal component basis for all images given the variations in both the illumination and the surface material. The principal component basis are constructed in such a way that all the symmetries (Helmholtz reciprocity and isotropy) of the BRDF are preserved in the basis functions. Using the framework we calculate a basis using a database of natural illumination and the CURET database containing BRDFs of real world surface materials.

We present a fully automatic algorithm for estimating the projected light source direction from a single image. The requirement is that there exists a segment of an occluding contour of an object with locally Lambertian surface reflectance in the image. The algorithm consists of three stages. First a heuristic algorithm picks out potential occluding contours using color and edge information. Secondly, for each contour the light source direction is estimated using a shading model. In the final stage the results from the estimations are fused together in a Bayesian network to arrive at the most likely light source direction. The probabilistic model takes into account that the contours from the first stage might not be occluding contours. Using the same framework the contours are also classified as occluding or not. Experiments test the second stage, estimating the light source direction from an occluding contour, as well as the full algorithm.