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 paper we determine the general solution of the equation [ f (x) + f (y)][ f (u) + f (v)] = f (xu − yv) + f (xv + yu) for all x, y, u,v ∈ ℝ without assuming any regularity condition on the u...

On a functional equation connected with a property of complex numbers

In this paper, we study the Hyers–Ulam stability of a simple Levi–Civita functional equation f(x+y)=f(x)h(y)+f(y) and its pexiderization f(x+y)= g(x) h(y)+k(y) on non-unital commutative semigroups by investigating the functional inequalities |f(x+y)−f(x)h(y)−f(y)|≤𝜖 and |f(x+y)−g(x)h(y)−k(y)|≤𝜖, respectively. We also study the bounded solutions of the simple Levi–Civita functional inequality.

Stability of a simple Levi–Civitá functional equation on non-unital commutative semigroups

This paper aims to study the Hyers-Ulam stability of a Sincov type functional equation $f(x,y) + f(y, z) + f(x, z) = \ell (x+y+z)$ when the domain of the functions is an abelian group and the range is a Banach space.

/pdf/stability-of-a-sincov-type-functional-equation-2ho4jwfbrj.pdf

Stability of A Sincov Type Functional Equation

Let S be a commutative semigroup, σ:S→S an endomorphism of order 2, G a 2-cancellative abelian group, and n a positive integer. One of the goals of this paper is to determine the general solutions of the functional equations f 1(x+y)+f 2(x+σy)=f 3(x) and also f 1(x+y)+f 2(x+σy)=f 3(x)+f 4(y) for all x,y∈S n , where f 1,f 2,f 3,f 4:S n →G are unknown functions. The results of this paper improve and generalize the earlier results due to Ebanks, Kannappan, and Sahoo (Can. Math. Bull. 35:321–327, 1992), and Bae and Park (J. Math. Anal. Appl. 326:1142–1148, 2007), and generalize the works of Sinopoulos (Aequ. Math. 59:255–261, 2000).

Jensen and Quadratic Functional Equations on Semigroups

In this paper, we give a new characterization of the Stolarsky means for two positive numbers. Our result generalizes a result due to Liu [5].

Prasanna K. Sahoo

Papers

On a functional equation connected with a property of complex numbers

Stability of a simple Levi–Civitá functional equation on non-unital commutative semigroups

Stability of A Sincov Type Functional Equation

Jensen and Quadratic Functional Equations on Semigroups

A characterization of the Stolarsky mean