Image Thresholding by Using Statistics for Determining the Number of Clusters

This paper aims to demonstrate that some statistics originally developed in cluster analysis for determining the number of clusters can be instead appropriately used in image thresholding to select optimal thresholds. Three highly-cited statistics, namely the Calinski-Harabasz index, the Gap statistic and the Silhouette widths, are chosen and applied to real images and simulated data, for illustrative purposes. The relationship between these statistics and a commonly-used image-thresholding method, Otsu’s method, is also briefly discussed.

[1]  Bülent Sankur,et al.  Survey over image thresholding techniques and quantitative performance evaluation , 2004, J. Electronic Imaging.

[2]  Prasanna K. Sahoo,et al.  Image thresholding using two-dimensional Tsallis-Havrda-Charvát entropy , 2006, Pattern Recognit. Lett..

[3]  D. M. Titterington,et al.  t -Tests, F -Tests and Otsu's Methods for Image Thresholding , 2011, IEEE Trans. Image Process..

[4]  Anil K. Jain,et al.  Goal-Directed Evaluation of Binarization Methods , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Robert Tibshirani,et al.  Estimating the number of clusters in a data set via the gap statistic , 2000 .

[6]  Nabih N. Abdelmalek,et al.  Maximum likelihood thresholding based on population mixture models , 1992, Pattern Recognit..

[7]  Nilanjan Ray,et al.  Pattern Recognition Letters , 1995 .

[8]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

[9]  G. W. Milligan,et al.  An examination of procedures for determining the number of clusters in a data set , 1985 .

[10]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[11]  Anil K. Jain.  Data clustering: 50 years beyond K-means , 2008, Pattern Recognit. Lett..

[12]  A. F. Adams,et al.  The Survey , 2021, Dyslexia in Higher Education.

[13]  Boris G. Mirkin,et al.  Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads , 2010, J. Classif..

[14]  Gurdial Arora,et al.  A thresholding method based on two-dimensional Renyi's entropy , 2004, Pattern Recognit..

[15]  Chris A. Glasbey,et al.  An Analysis of Histogram-Based Thresholding Algorithms , 1993, CVGIP Graph. Model. Image Process..

[16]  P.K Sahoo,et al.  A survey of thresholding techniques , 1988, Comput. Vis. Graph. Image Process..

[17]  André Hardy,et al.  An examination of procedures for determining the number of clusters in a data set , 1994 .

[18]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[19]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.