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A new feature (the complement feature) is proposed in an Eigen formulations for performing global image thresholding. The goal is to find an intensity or gray-level value below which is the background while above it is the foreground (object). Each pixel in the image is represented by a (2D) unit vector where the x-component is the normalized (to [0,1] or [-1,1]) intensity of the pixel, while the y-component is its complement (e.g., Euclidian L2-Norm). The correlation matrix can then constructed to find the cross-correlation, Eigen vectors (axes of inertia) and Eigen values (description of respective sizes). Several implementations for each of the three previously mentioned categories are proposed to perform image thresholding. Interestingly, some of the proposed implementations do not require exhaustive search and a direct solution can be obtained. The results are promising on a wide range of images as demonstrated by comparison with the well-known Otsu method.

This paper proposes several novel schemes for image thresholding. The idea is simply to compare the original image histogram to that of the thresholded image. Element by element comparison (sum of absolute difference between the two histograms) is found to be of better performance than a single feature (area or size) comparison. The optimum threshold is the one producing the best comparison. Cumulative histogram is introduced as a generalization to the area under the curve and found to be of better performance. In addition, a new performance measure is suggested based on percentage of correct assignments in both foreground and background. Comparative results with Otsu shows the effectiveness of the proposed schemes.

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