Eigenstructure involving the histogram for image thresholding

The idea of the proposed image thresholding scheme is simply to consider the histogram as a 2D plot rather than a 1D function. The data can now be represented as a two‐row matrix. The first row is simply the grey levels of the image and the second row is the corresponding histogram values. Multiplying this matrix by its transpose will result in a power‐type matrix of size 2 × 2. The best threshold is the one producing a power matrix closer to that of the original image. Many combinations of the eigenvalues are suggested. To increase the correlation with the first row of the matrix, the histogram is replaced by the cumulative histogram. It is noticed that the trace of the matrix produces the best results. Comparative results show the effectiveness of the proposed schemes.