An Information Theory framework for two-stage binary image operator design

Santos, Carlos Silva; Hirata, Nina S. T.; Hirata, Roberto

doi:10.1016/j.patrec.2009.03.019

Cited by 13 publications

(7 citation statements)

References 20 publications

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“…The W-operators are a class of nonlinear operators, within the domain of Computational Mathematical Morphology [1,2]. The designing process of these operators is based on the estimation of joint probabilities [3], or conditional probabilities [4], for the patterns viewed by a given window. The estimation is made from training examples, formed by pairs of observed and ideal images.…”

Section: Introductionmentioning

confidence: 99%

“…It occurs when certain patterns are not found during training. Some approaches have been proposed to circumvent this problem such as: automatic programming of binary morphological machines, pyramidal multiresolution [1], decision trees, genetic algorithms, adaptive algorithms, incremental splitting intervals (ISI), and multilevel training [3].…”

Section: Introductionmentioning

confidence: 99%

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Automatic Design of Binary W-Operators Using Artificial Feed-Forward Neural Networks Based on the Weighted Mean Square Error Cost Function

Benalcázar

Brun

Ballarin

et al. 2012

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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One of the main issues concerning automatic design of W-operators is the one of generalization. Considering the designing of W-operators as a particular case of designing a pattern recognition system, in this work we propose a new approach for the automatic design of binary W-operators. This approach consists on a functional representation of the conditional probabilities for the whole set of patterns viewed by a given window, instead the values of the characteristic function. The estimation of its parameters is achieved by means of a nonlinear regression performed by an artificial feed-forward neural network based on a weighted mean square error cost function. Experimental results show that, for the applications presented in this work, the proposed approach leads to better results than one of the best existing methods of generalization within the family of W-operators, like is the case of pyramidal multiresolution.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automatic Design of Binary W-Operators Using Artificial Feed-Forward Neural Networks Based on the Weighted Mean Square Error Cost Function

Benalcázar

Brun

Ballarin

et al. 2012

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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“…Apesar de ser um avanço, o projeto em dois níveis ainda requer a escolha do número e da forma das subjanelas, um processo que pode ser bastante trabalhoso se realizado manualmente. Neste capítulo, um método para a automação desse processo será apresentado, originalmente proposto em [SHJ10]. Mas antes disso, o projeto de um operador de dois níveis será discutido em maior detalhe.…”

Section: Operadores De Imagens Bináriasunclassified

Construção de atributos binários baseada em análise de interações

Santos¹

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This work addresses the task of feature extraction for classification when both labels and features are binary. Our approach aims to build features with reduced interaction effects, thus relieving the classifiers from dealing explicitly with interactions. We introduce a new technique for building binary features by means of a parity calculating matrix that changes the coordinates of a binary vector. That matrix can be built purposefully for manipulating specific information theoretic measures. The resulting transform gives rise to groups of binary variables. A new algorithm for independent component analysis of binary features is proposed, based on this technique. In the context of classification, a new algorithm is presented that reduces the conditional dependence of features, given the label. A third algorithm presented in this text reduces the Interaction Information between pairs of features, a measure associated with redundancy or collaboration among predictors. This algorithm is used in the context of designing two-level operators for binary images. This type of operator combines the responses of several first-level operators to create the output image. In this case, the interaction reducing algorithm handles the division of the image into subregions. A complete framework for designing these operators is provided, involving feature selection and model comparison techniques. Experimental results show that the proposed method generates more accurate operators, compared to the single-level ones.

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“…The method presented in [SHH10] (referred here as IT) uses the three-way Interaction Information [McG54] (Eq. 5.2) to group individual points into windows, where I(Y ; X) is the Mutual Information between Y and X, where X is a set of independent variables and Y is the dependent variable.…”

Section: Previous Approachesmentioning

confidence: 99%

“…Many works [SHH10, DH15,MHH16] have used feature selection techniques to determine windows for two-level operators. Feature selection can be used to determine first-level windows inside a large domain window D, as in [SHH10,MHH16], or to select which operators to combine from a set of candidates [DH15,MHH16]. In general, window determination and classifier training are regarded as separate tasks.…”

Section: Introductionmentioning

confidence: 99%

W-operator learning using linear models for both gray-level and binary inputs

Montagner¹

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MONTAGNER, Igor S., W -operator learning using linear models for both gray-level and binary inputs, 2017. Thesis (Phd) -Image Processing techniques can be used to solve a broad range of problems, such as medical imaging, document processing and object segmentation. Image operators are usually built by combining basic image operators and tuning their parameters. This requires both experience in Image Processing and trial-and-error to get the best combination of parameters.An alternative approach to design image operators is to estimate them from pairs of training images containing examples of the expected input and their processed versions. By restricting the learned operators to those that are translation invariant and locally defined (W -operators) we can apply Machine Learning techniques to estimate image transformations. The shape that defines which neighbors are used is called a window.W -operators trained with large windows usually overfit due to the lack sufficient of training data. This issue is even more present when training operators with gray-level inputs. Although approaches such as the twolevel design, which combines multiple operators trained on smaller windows, partly mitigates these problems, they also require more complicated parameter determination to achieve good results.In this work we present techniques that increase the window sizes we can use and decrease the number of manually defined parameters in Woperator learning. The first one, KA, is based on Support Vector Machines and employs kernel approximations to estimate image transformations. We also present adequate kernels for processing binary and gray-level images. The second technique, NILC, automatically finds small subsets of operators that can be successfully combined using the two-level approach.Both methods achieve competitive results with methods from the literature in two different application domains. The first one is a binary document processing problem common in Optical Music Recognition, while the second is a segmentation problem in gray-level images. The same techniques were applied without modification in both domains.

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An Information Theory framework for two-stage binary image operator design

Cited by 13 publications

References 20 publications

Automatic Design of Binary W-Operators Using Artificial Feed-Forward Neural Networks Based on the Weighted Mean Square Error Cost Function

Automatic Design of Binary W-Operators Using Artificial Feed-Forward Neural Networks Based on the Weighted Mean Square Error Cost Function

Construção de atributos binários baseada em análise de interações

W-operator learning using linear models for both gray-level and binary inputs

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