An Epipolar Line from a Single Pixel

Computing the epipolar geometry from feature points between cameras with very different viewpoints is often error prone, as an object's appearance can vary greatly between images. For such cases, it has been shown that using motion extracted from video can achieve much better results than using a static image. This paper extends these earlier works based on the scene dynamics. In this paper we propose a new method to compute the epipolar geometry from a video stream, by exploiting the following observation: For a pixel p in Image A, all pixels corresponding to p in Image B are on the same epipolar line. Equivalently, the image of the line going through camera A's center and p is an epipolar line in B. Therefore, when cameras A and B are synchronized, the momentary images of two objects projecting to the same pixel, p, in camera A at times t1 and t2, lie on an epipolar line in camera B. Based on this observation we achieve fast and precise computation of epipolar lines. Calibrating cameras based on our method of finding epipolar lines is much faster and more robust than previous methods.Comment: WACV 201

Efficient and Accurate Gaussian Image Filtering Using Running Sums

This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the error function used for kernel approximation and its relation to the properties of the input signal. Based on natural image statistics we propose a quadratic form kernel error function so that the output image l2 error is minimized. We apply the proposed approach to approximate the Gaussian kernel by linear combination of constant functions. This results in very efficient Gaussian filtering method. Our experiments show that the proposed technique is faster than state of the art methods while preserving a similar accuracy

Intrinsic Volumes of Random Cubical Complexes

Intrinsic volumes, which generalize both Euler characteristic and Lebesgue volume, are important properties of $d$-dimensional sets. A random cubical complex is a union of unit cubes, each with vertices on a regular cubic lattice, constructed according to some probability model. We analyze and give exact polynomial formulae, dependent on a probability, for the expected value and variance of the intrinsic volumes of several models of random cubical complexes. We then prove a central limit theorem for these intrinsic volumes. For our primary model, we also prove an interleaving theorem for the zeros of the expected-value polynomials. The intrinsic volumes of cubical complexes are useful for understanding the shape of random $d$-dimensional sets and for characterizing noise in applications.Comment: 17 pages with 7 figures; this version includes a central limit theore