Shape reasoning on mis-segmented and mis-labeled objects using approximated Fisher criterion

To automatically determine semantics of a shape or to generate a set of keywords that describe the content of a given image is a difficult problem due to: (a) the high-dimensional problem, (b) the unsolved automatic object segmentation (mis-segmentation), and (c) the lack of well-labeled large image database (mis-labeling). In order to tackle (a), despite (b), (c) and the expensive handy image segmentation and labeling, visual features should be automatically selected to convey the most robust and discriminant information without requiring too computational cost. Therefore, we propose a novel method: 'Approximation of Linear Discriminant Analysis' (ALDA), which is more generic than LDA: ALDA does not require explicit class labeling of each training samples. We theoretically show that under weak assumption, ALDA allows efficient ranking estimation of the discriminant powers of the visual features. We apply ALDA on COREL database (10K images, 267 words) with Normalized Cuts segmentation algorithm. First, we demonstrate an image classification gain of 43%, while reducing features set by a factor 10. Secondly, we demonstrate that for some words (like 'Door', 'Flag'), even low-level shape features (convex hull, or moment of inertia) are more discriminant than any color or texture features.