Matching of high-dimensional features using nearest neighbors search is an important part of image matching methods which are based on local invariant features. In this work we highlight effects pertinent to high-dimensional spaces that are significant for matching, yet have not been explicitly accounted for in previous work. In our approach, we require every nearest neighbor to be meaningful, that is, sufficiently close to a query feature such that it is an out-lier to a background feature distribution. We estimate the background feature distribution from the extended neighborhood of a query feature given by its k nearest neighbors. Based on the concept of meaningful nearest neighbors, we develop a novel high-dimensional feature matching method and evaluate its performance by conducting image matching on two challenging image data sets. A superior performance in terms of accuracy is shown in comparison to several state-of-the-art approaches. Additionally, to make search for k nearest neighbors more efficient, we develop a novel approximate nearest neighbors search method based on sparse coding with an overcomplete basis set that provides a ten-fold speed-up over an exhaustive search even for high dimensional spaces and retains excellent approximation to an exact nearest neighbors search.

We present a new theory that shows that two images of the same object taken under two different light directions can be made virtually identical by filtering each image by a directional derivative filter. The direction and magnitude of the derivative is generally different for each image, and depends on illumination directions used. The method requires the object surface to be of uniform Lambertian reflectance and a shallow relief, and the light directions used to be sufficiently inclined from the surface macro-normal. For a specific case when the surface consists of spherical patches, the two images can be made identical, for any two light directions used provided that none of them is perpendicular to the viewing axis. We provide some simple experiments which illustrate the validity of this theory. 1

This paper develops new theory for the optimal placement of photometric stereo lighting in the presence of camera noise. We show that for three lights, any triplet of orthogonal light directions minimises the uncertainty in scaled normal computation. The assumptions are that the camera noise is additive and normally distributed, and uncertainty is defined as the expectation of squared distance of scale normal to the ground truth. If the camera noise is of zero mean and variance sigma2the optimal (minimum) uncertainty in the scaled normal is 3sigma2For case of n > 3 lights, we show that the minimum uncertainty is 9sigma2n, and identify sets of light configurations which reach this theoretical minimum

Lambertian photometric stereo with unknown light source parameters is ambiguous. Provided that the object imaged constitutes a surface, the ambiguity is represented by the group of generalised bas-relief (GBR) transformations. We show that this ambiguity is resolved when specular reflection is present in two images taken under two different light source directions. We identify all configurations of the two directional lights which are singular and show that they can easily be tested for. While previous work used optimisation algorithms to apply the constraints implied by the specular reflectance component, we have developed a linear algorithm to achieve this goal. Our theory can be utilised to construct fast algorithms for automatic reconstruction of smooth glossy surfaces.