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

Additive and biadditive functions Langrange's mean value theorem and related functional equations Pompeiu's mean value theorem and associated functional equations two-dimensional mean value theorems and functional equations some generalizations of Lagrange's mean value theorem mean value theorems for some generalized derivatives some integral mean value theorems and related topics.

/pdf/mean-value-theorems-and-functional-equations-3esb4rz37q.pdf

Mean Value Theorems and Functional Equations

Image thresholding using two-dimensional Tsallis-Havrda-Charvát entropy

Additive Cauchy Functional Equation Introduction Functional Equations Solution of Additive Cauchy Functional Equation Discontinuous Solution of Additive Cauchy Equation Other Criteria for Linearity Additive Functions on the Complex Plane Concluding Remarks Exercises Remaining Cauchy Functional Equations Introduction Solution of Exponential Cauchy Equation Solution of Logarithmic Cauchy Equation Solution of Multiplicative Cauchy Equation Concluding Remarks Exercises Cauchy Equations in Several Variables Introduction Additive Cauchy Equations in Several Variables Multiplicative Cauchy Equations in Several Variables Other Two Cauchy Equations in Several Variables Concluding Remarks Exercises Extension of the Cauchy Functional Equations Introduction Extension of Additive Functions Concluding Remarks Exercises Applications of Cauchy Functional Equations Introduction Area of Rectangles Definition of Logarithm Simple and Compound Interests Radioactive Disintegration Characterization of Geometric Distribution Characterization of Discrete Normal Distribution Characterization of Normal Distribution Concluding Remarks More Applications of Functional Equations Introduction Sum of Powers of Integers Sum of Powers of Numbers on Arithmetic Progression Number of Possible Pairs Among n Things Cardinality of a Power Set Sum of Some Finite Series Concluding Remarks The Jensen Functional Equation Introduction Convex Function The Jensen Functional Equation A Related Functional Equation Concluding Remarks Exercises Pexider's Functional Equations Introduction Pexider's Equations Pexiderization of the Jensen Functional Equation A Related Equation Concluding Remarks Exercises Quadratic Functional Equation Introduction Biadditive Functions Continuous Solution of Quadratic Functional Equation A Representation of Quadratic Functions Contents xvii Pexiderization of Quadratic Equation Concluding Remarks Exercises D'Alembert Functional Equation Introduction Continuous Solution of d'Alembert Equation General Solution of d'Alembert Equation A Characterization of Cosine Functions Concluding Remarks Exercises Trigonometric Functional Equations Introduction Solution of a Cosine-Sine Functional Equation Solution of a Sine-Cosine Functional Equation Solution of a Sine Functional Equation Solution of a Sine Functional Inequality An Elementary Functional Equation Concluding Remarks Exercises Pompeiu Functional Equation Introduction General Solution Pompeiu Functional Equation A Generalized Pompeiu Functional Equation Pexiderized Pompeiu Functional Equation Concluding Remarks Exercises Hosszu Functional Equation Introduction Hosszu Functional Equation A Generalization of Hosszu Equation Concluding Remarks Exercises Davison Functional Equation Introduction Continuous Solution of Davison Functional Equation General Solution of Davison Functional Equation Concluding Remarks Exercises Abel Functional Equation Introduction General Solution of Abel Functional Equation Concluding Remarks Exercises Mean Value Type Functional Equations Introduction The Mean Value Theorem A Mean Value Type Functional Equation Generalizations of Mean Value Type Equation Concluding Remarks Exercises Functional Equations for Distance Measures Introduction Solution of two functional equations Some Auxiliary Results Solution of a generalized functional equation Concluding Remarks Exercises Stability of Additive Cauchy Equation Introduction Cauchy Sequence and Geometric Series Hyers Theorem Generalizations of Hyers Theorem Concluding Remarks Exercises Stability of Exponential Cauchy Equations Introduction Stability of Exponential Equation Ger Type Stability of Exponential Equation Concluding Remarks Exercises Stability of d'Alembert and Sine Equations Introduction Stability of d'Alembert Equation Stability of Sine Equation Concluding Remarks Exercises Stability of Quadratic Functional Equations Introduction Stability of the Quadratic Equation Stability of Generalized Quadratic Equation Stability of a Functional Equation of Drygas Concluding Remarks Exercises Stability of Davison Functional Equation Introduction Stability of Davison Functional Equation Generalized Stability of Davison Equation Concluding Remarks Exercises Stability of Hosszu Functional Equation Introduction Stability of Hossz_u Functional Equation Stability of Pexiderized Hossz_u Functional Equation Concluding Remarks Exercises Stability of Abel Functional Equation Introduction Stability Theorem Concluding Remarks Exercises Bibliography Index

Introduction to Functional Equations

In this paper, we will prove the Hyers-Ulam stability of the quadratic functional equation of Pexider type, f1(x + y) + f2(x y) = f3(x) + f4(y).

Hyers-ulam stability of the quadratic equation of pexider type

Medical Imaging Systems Fundamental Tools for Image Processing and Analysis Probability Theory for Stochastic Modeling of Images Two-Dimensional Fourier Transform Nonlinear Diffusion Filtering Intensity-Based Image Segmentation Image Segmentation by Markov Random Field Modeling Deformable Models Image Analysis Application 1: Quantification of Green Fluorescent Protein eXpression in Live Cells: ProXcell Application 2: Calculation of Performance Parameters of Gamma Cameras and SPECT Systems Application 3: Analysis of Islet Cells Using Automated Color Image Analysis Appendix A: Notation Appendix B: Working with DICOM Images Appendix C: Medical Image Processing Toolbox Appendix D: Description of Image Data

Prasanna K. Sahoo

Papers

Mean Value Theorems and Functional Equations

Image thresholding using two-dimensional Tsallis-Havrda-Charvát entropy

Introduction to Functional Equations

Hyers-ulam stability of the quadratic equation of pexider type

Image Processing with Matlab: Applications in Medicine and Biology