A Fisher-Rao metric for paracatadioptric images of lines

In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied. The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and based on the Hough transform

Cramer-Rao Lower Bound and Information Geometry

This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbreaking paper, which had a profound impact on subsequent statistical research.Comment: To appear in Connected at Infinity II: On the work of Indian mathematicians (R. Bhatia and C.S. Rajan, Eds.), special volume of Texts and Readings In Mathematics (TRIM), Hindustan Book Agency, 201

Information Geometric Approach to Bayesian Lower Error Bounds

Information geometry describes a framework where probability densities can be viewed as differential geometry structures. This approach has shown that the geometry in the space of probability distributions that are parameterized by their covariance matrix is linked to the fundamentals concepts of estimation theory. In particular, prior work proposes a Riemannian metric - the distance between the parameterized probability distributions - that is equivalent to the Fisher Information Matrix, and helpful in obtaining the deterministic Cram\'{e}r-Rao lower bound (CRLB). Recent work in this framework has led to establishing links with several practical applications. However, classical CRLB is useful only for unbiased estimators and inaccurately predicts the mean square error in low signal-to-noise (SNR) scenarios. In this paper, we propose a general Riemannian metric that, at once, is used to obtain both Bayesian CRLB and deterministic CRLB along with their vector parameter extensions. We also extend our results to the Barankin bound, thereby enhancing their applicability to low SNR situations.Comment: 5 page