PNC in 4D Object and Multi-Dimensional Data Modeling

PNC in 4D Object and Multi-Dimensional Data Modeling

DOI: 10.4018/978-1-5225-2531-8.ch006
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Proposed method, called Probabilistic Features Combination (PFC), is the method of N-dimensional data interpolation and extrapolation using the set of key points (knots or nodes). The method of Probabilistic Features Combination (PFC) enables interpolation and modeling of high-dimensional data using features' combinations and different coefficients ? as modeling function. Functions for ? calculations are chosen individually at each data modeling and it is treated as N-dimensional probability distribution function: ? depends on initial requirements and features' specifications. PFC method leads to data interpolation as handwriting or signature identification and image retrieval via discrete set of feature vectors in N-dimensional feature space. So PFC method makes possible the combination of two important problems: interpolation and modeling in a matter of image retrieval or writer identification. PFC interpolation develops a linear interpolation in multidimensional feature spaces into other functions as N-dimensional probability distribution functions.
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Introduction And Background

Multidimensional data modeling appears in many branches of science and industry. Image retrieval, data reconstruction, object identification or pattern recognition are still the open problems in artificial intelligence and computer vision. The chapter is dealing with these questions via modeling of high-dimensional data for applications of image segmentation in image retrieval and recognition tasks. Handwriting based author recognition offers a huge number of significant implementations which make it an important research area in pattern recognition. There are so many possibilities and applications of the recognition algorithms that implemented methods have to be concerned on a single problem: retrieval, identification, verification or recognition. This chapter is concerned with two parts: image retrieval and recognition tasks. Image retrieval is based on probabilistic modeling of unknown features via combination of N-dimensional probability distribution function for each feature treated as random variable. Handwriting and signature recognition and identification represents a significant problem. In the case of biometric writer recognition, each person is represented by the set of modeled letters or symbols. The sketch of proposed Probabilistic Features Combination (PFC) method consists of three steps: first handwritten letter or symbol must be modeled by a vector of features (N-dimensional data), then compared with unknown letter and finally there is a decision of identification. Author recognition of handwriting and signature is based on the choice of feature vectors and modeling functions. So high-dimensional data interpolation in handwriting identification (Marti & Bunke, 2002) is not only a pure mathematical problem but important task in pattern recognition and artificial intelligence such as: biometric recognition (Nosary, Heutte & Paquet, 2004), personalized handwriting recognition (Djeddi & Souici-Meslati, 2010 & 2011), automatic forensic document examination (Van, Vuurpijl, Franke & Schomaker, 2005; Schomaker, Franke & Bulacu, 2007), classification of ancient manuscripts (Siddiqi, Cloppet & Vincent, 2009). Also writer recognition (Garain & Paquet, 2009) in monolingual handwritten texts (Ozaki, Adachi & Ishii, 2006) is an extensive area of study (Chen, Lopresti & Kavallieratou, 2010) and the methods independent from the language (Chen, Cheng & Lopresti, 2011) are well-seen (Bulacu, Schomaker & Brink, 2007).

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