We conduct an exhaustive survey of image thresholding methods, categorize them, express their formulas under a uniform notation, and finally carry their performance comparison. The thresholding methods are categorized according to the information they are exploiting, such as histogram shape, measurement space clustering, entropy, object attributes, spatial correlation, and local gray-level surface. 40 selected thresholding methods from various categories are compared in the context of nondestructive testing applications as well as for document images. The comparison is based on the combined performance measures. We identify the thresholding algorithms that perform uniformly better over nonde- structive testing and document image applications. © 2004 SPIE and IS&T. (DOI: 10.1117/1.1631316)

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Survey over image thresholding techniques and quantitative performance evaluation

A review on image segmentation techniques

We present here a new algorithm for segmentation of intensity images which is robust, rapid, and free of tuning parameters. The method, however, requires the input of a number of seeds, either individual pixels or regions, which will control the formation of regions into which the image will be segmented. In this correspondence, we present the algorithm, discuss briefly its properties, and suggest two ways in which it can be employed, namely, by using manual seed selection or by automated procedures. >

Seeded region growing

In digital image processing, thresholding is a well-known technique for image segmentation. Because of its wide applicability to other areas of the digital image processing, quite a number of thresholding methods have been proposed over the years. In this paper, we present a survey of thresholding techniques and update the earlier survey work by Weszka (Comput. Vision Graphics & Image Process 7, 1978 , 259–265) and Fu and Mu (Pattern Recognit. 13, 1981 , 3–16). We attempt to evaluate the performance of some automatic global thresholding methods using the criterion functions such as uniformity and shape measures. The evaluation is based on some real world images.

http://pequan.lip6.fr/~bereziat/pima/2012/seuillage/sahoo88.pdf

A survey of thresholding techniques

Handwriting has continued to persist as a means of communication and recording information in day-to-day life even with the introduction of new technologies. Given its ubiquity in human transactions, machine recognition of handwriting has practical significance, as in reading handwritten notes in a PDA, in postal addresses on envelopes, in amounts in bank checks, in handwritten fields in forms, etc. This overview describes the nature of handwritten language, how it is transduced into electronic data, and the basic concepts behind written language recognition algorithms. Both the online case (which pertains to the availability of trajectory data during writing) and the off-line case (which pertains to scanned images) are considered. Algorithms for preprocessing, character and word recognition, and performance with practical systems are indicated. Other fields of application, like signature verification, writer authentification, handwriting learning tools are also considered.

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Online and off-line handwriting recognition: a comprehensive survey

In this paper we establish the stability of Jensen’s functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and T (2, K), where K is an arbitrary commutative field with characteristic different from two. We also prove that any group A can be embedded into some group G such that the Jensen functional equation is stable on G.

On the stability of Jensen’s functional equation on groups

General solution of some functional equations related to the determinant of some symmetric matrices

The problem of the Hyers-Ulam stability of the Hermite-Hadamard inequality posed by Zs. Páles is solved. It is shown that for continuous functions f : I → R neither the inequality f ( x+y 2 ) 1 y−x ∫ y x f (t) dt + nor 1 y−x ∫ y x f (t) dt f (x)+f (y) 2 + implies the c − convexity of f (with any c > 0 ). However, if f is continuous and satisfies both of the above inequalities simultaneously, then it is 4 -convex. Mathematics subject classification (2000): 39B82, 26A51.

/pdf/the-stability-problem-of-the-hermite-hadamard-inequality-3vsyly38lg.pdf

The stability problem of the Hermite-Hadamard inequality

Limit Properties of Differential Mean Values

In digital image analysis, edge detection, line detection, texture classification, and so forth are basic to image understanding and interpretation. Since a typical image is void of predetermined directions of edge, line, or texture, rotation invariant filters are important for their detection. In designing such filters the concept of rotation invariant separable function is often used. Here it is shown that every rotation invariant separable real valued function of two variables is either Gaussian or identically zero. This justifies the use of Gaussian filters in image processing. Furthermore, while deriving this result, the authors obtained the general solutions of two functional equations considered by Swiatak in 1975. Swiatak found the solutions when one of the unknown functions is continuous at zero. No regularity assumptions were made and all the general solutions that contain the solution obtained in [Aequationes Math., 12 (1975), pp. 39–64] were determined.

Prasanna K. Sahoo

Papers

On the stability of Jensen’s functional equation on groups

General solution of some functional equations related to the determinant of some symmetric matrices

The stability problem of the Hermite-Hadamard inequality

Limit Properties of Differential Mean Values

Rotation invariant separable functions are Gaussian