the two characteristic vectors out of the infinite set of vec-.~ .~ ..One of the key tools in physics-based vision has been color histogram analysis. But to date histograms have only been used for pixel grouping, color analysis, and material type labeling. In this paper we present a new, quantitative model of histograms that yields a more complete description of scene properties.In the mid-1980s it was recognized that the color variation for inhomogeneous surfaces may be modeled as a regular physical process with a planar distribution in color space. However, the colors do not fall randomly in aplane, but form clusters at specijic points in color space. The location, dimensions, and orientation of these clusters directly relate to many scene properties. A full analysis of the histogram leads to a description of surface roughness and imaging geometry, as well as an improved estimate of illumination color and object color.

Automatic extraction of vertebra regions from a spinal magnetic resonance (MR) image is normally required as the first step to an intelligent spinal MR image diagnosis system. In this work, we develop a fully automatic vertebra detection and segmentation system, which consists of three stages; namely, AdaBoost-based vertebra detection, detection refinement via robust curve fitting, and vertebra segmentation by an iterative normalized cut algorithm. In order to produce an efficient and effective vertebra detector, a statistical learning approach based on an improved AdaBoost algorithm is proposed. A robust estimation procedure is applied on the detected vertebra locations to fit a spine curve, thus refining the above vertebra detection results. This refinement process involves removing the false detections and recovering the miss-detected vertebrae. Finally, an iterative normalized-cut segmentation algorithm is proposed to segment the precise vertebra regions from the detected vertebra locations. In our implementation, the proposed AdaBoost-based detector is trained from 22 spinal MR volume images. The experimental results show that the proposed vertebra detection and segmentation system can achieve nearly 98% vertebra detection rate and 96% segmentation accuracy on a variety of testing spinal MR images. Our experiments also show the vertebra detection and segmentation accuracies by using the proposed algorithm are superior to those of the previous representative methods. The proposed vertebra detection and segmentation system is proved to be robust and accurate so that it can be used for advanced research and application on spinal MR images.

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