A fast two-dimensional entropic thresholding algorithm

Segmentation of X‐ray computed tomography images of porous materials: A crucial step for characterization and quantitative analysis of pore structures

“…SP-Chen also uses maximum entropy considerations, but relies on the two-dimensional histogram that is constructed utilizing not only the local intensity value of each voxel but also the average value in a certain neighborhood centered at that voxel (3 Â 3 Â 3 region was used for this study). This method was originally proposed by Abutaleb [1989] and further improved by Brink [1992], with an optimized solution scheme provided by Chen et al [1994]. SP-Pal employs the voxel co-occurrence data to find the threshold that maximizes the sum of Shannon's entropies of the within-class co-occurrences of background and foreground voxel classes [Pal and Pal, 1989;Chang et al, 2006].…”

Image Thresholding by Maximizing the Index of Nonfuzziness of the 2-D Grayscale Histogram

“…In the work that followed, Brink improved Abutaleb's method by maximizing the class entropies, which was achieved by using a single threshold vector to maximize the entropy derived from both the background and the object classes [20]. To speed up the process, Chen et al proposed a fast two-phase algorithm to reduce computing time from [21]. In the first phase, a set of quantized threshold vectors was obtained by Brink's method.…”

A New Approach for Thresholding Finger Print Images based on Second Order Statistical Methods

“…Other, some 1D thresholding techniques extend from bi-level threshold selection to multilevel threshold selection [19,23]. In contrast to 1D thresholding methods, 2D methods essentiall do image segmentation by using spatial information in an image [28][29][30][31][32][33]. Kirby and Rosenfeld proposed a 2D thresholding method that simultaneously considers both the pixel gray level and the local statistics of its neighboring pixels [30].…”

“…However, their method is very time-consuming at determining the 2D total entropy of the resulting two classes. As a result, Chen et al, proposed a two-stage approach to search for the optimal threshold of 2D entropic thresholding so that the computation complexity can be reduced to O(L8/3) for an image with L gray levels [28]. Recently, Gong et al, [29] designed a recursive algorithm for 2D entropic thresholding to further reduce the computation complexity to O(L2).…”