Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Improved recognition of aged Kannada documents by effective segmentation of merged characters

In optical character recognition of very old books, the recognition accuracy drops mainly due to the merging or breaking of characters. In this paper, we propose the first algorithm to segment merged Kannada characters by using a hypothesis to select the positions to be cut. This method searches for the best possible positions to segment, by taking into account the support vector machine classifier's recognition score and the validity of the aspect ratio (width to height ratio) of the segments between every pair of cut positions. The hypothesis to select the cut position is based on the fact that a concave surface exists above and below the touching portion. These concave surfaces are noted down by tracing the valleys in the top contour of the image and similarly doing it for the image rotated upside-down. The cut positions are then derived as closely matching valleys of the original and the rotated images. Our proposed segmentation algorithm works well for different font styles, shapes and sizes better than the existing vertical projection profile based segmentation. The proposed algorithm has been tested on 1125 different word images, each containing multiple merged characters, from an old Kannada book and 89.6% correct segmentation is achieved and the character recognition accuracy of merged words is 91.2%. A few points of merge are still missed due to the absence of a matched valley due to the specific shapes of the particular characters meeting at the merges.