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.

/pdf/online-and-off-line-handwriting-recognition-a-comprehensive-4qmt9ty596.pdf

Online and off-line handwriting recognition: a comprehensive survey

In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degree β. Here, we find the general solution of the functional equation (2) on an open domain, without using 0-probability and 1-probability.

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On the general solution of a functional equation connected to sum form information measures on open domain—III

A characterization of low degree polynomials

In this paper, we determine the general solution of the functional equations y(=:++,)=p()+q()+()h(), (V. e .) and f(ax + by + cxy) f(x) + f(y) "4- f(x)f(y), (V x, y 6 . which are generalizations of a functional equation studied by Pompeiu. We present a method which is simple and direct to determine the general solutions of the above equations without any regularity assumptions.

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On generalizations of the Pompeiu functional equation

Let 
$ f: G \times G \to {\Bbb C} $
 , where G denotes a 2-divisible abelian group and 
$ {\Bbb C} $
 the set of complex numbers. The general solution of the functional equation¶¶f(x + t,y + t) + f(x - t,y) + f(x,y - t) = f(x - t,y - t) + f(x,y + t) + f(x + t,y)¶ for all x,y,t in G is determined. It is shown that the solution of this functional equation is of the form 
$ f(x,y) = B(x,y)+\varphi(x) + \psi(y) + \chi (x-y) $
 , where the map 
$ B : G \times G \to {\Bbb C} $
 is biadditive and 
$ \varphi, \psi, \chi :G\to{\Bbb C} $
 are arbitrary functions.

On a functional equation related to digital filtering

Let $G$ be a group and $H$ an abelian group Let $J^{*} (G, H)$ be the set of solutions $f \colon G \to H$ of the Jensen functional equation $f(xy)+f(xy^{-1}) = 2f(x)$ satisfying the condition $f(xyz) - f(xzy) = f(yz)-f(zy)$ for all $x, y , z \in G$ Let $Q^{*} (G, H)$ be the set of solutions $f \colon G \to H$ of the quadratic equation $f(xy)+f(xy^{-1}) = 2f(x) + 2f(y)$ satisfying the Kannappan condition $f(xyz) = f(xzy)$ for all $x, y, z \in G$ In this paper we determine solutions of the Whitehead equation on groups We show that every solution $f \colon G \to H$ of the Whitehead equation is of the form $4f = 2 \varphi + 2 \psi $, where $2\varphi \in J^* (G, H)$ and $2\psi \in Q^* (G, H)$ Moreover, if $H$ has the additional property that $2h = 0$ implies $h = 0$ for all $h \in H$, then every solution $f \colon G \to H$ of the Whitehead equation is of the form $2f = \varphi + \psi $, where $\varphi \in J^*(G,H)$ and $2\psi (x) = B(x, x)$ for some symmetric bihomomorphism $B \colon G \times G \to H$

/pdf/solution-of-whitehead-equation-on-groups-3lkp866hmj.pdf

Prasanna K. Sahoo

Papers

On the general solution of a functional equation connected to sum form information measures on open domain—III

A characterization of low degree polynomials

On generalizations of the Pompeiu functional equation

On a functional equation related to digital filtering

Solution of Whitehead equation on groups