Context-Based Support Vector Machine Using Spatial Autocorrelation Function for Image Classification Rog´erio G. Negri1 , Eliana Pantale˜ao1 1
Instituto Nacional de Pesquisas Espaciais – Divis˜ao de Processamento de Imagens Caixa Postal 515 – S˜ao Jos´e dos Campos – SP – Brazil {rogerio,elianap}@dpi.inpe.br
Abstract. Support vector machine classifiers are widely used in pattern recognition applications. Contextual information can improve the classifier accuracy for image classification. The autocorrelation function can be used to estimate how relevant the neighborhood information is for a pixel classification. This paper proposes a support vector machine classifier that uses contextual information of the discriminant function for one-against-all multiclass strategy. The spatial autocorrelation function of the discriminant matrix is used to build a filter mask that will include the contextual information in the classification process.
1. Introduction Support vector machines have been successfully used in several application areas, and specially for pattern recognition. Since they were developed by Vapnik [Vapnik 1995], many variations of SVM classifiers were created, with many different purposes, such as in [Leea et al. 2005], [Jayadeva et al. 2007] and [Liu et al. 2006]. Contextual information is used by Bruzzone et al. [Bruzzone et al. 2008] through the addition of a contextual term in the objective function. In the presence of noisy or non-separable data, a non-contextual pixel classifier can label single pixels with a different class from the neighborhood. Contextual information gives a significant hint about the pixel class in this case. Therefore, the information about the pixel neighborhood can be used to improve the classifier accuracy. This helps to avoid undesired isolated pixels and make the objects edges more clearly defined. The spatial autocorrelation function can be used to measure the similarity degree of the values in the image, according to the distance of the pixels. An image with big homogeneous regions would result in a very different function from a very noisy or small textured image. Hence, it can be used to determine the size of the neighborhood that can be considered when classifying a pixel. This paper proposes a support vector machine classifier that uses the autocorrelation function of the one-against-all discriminants to evaluate how relevant the neighborhood information is for pixel classification. Contextual information is included by filtering the discriminant matrix. The results showed that the autocorrelation function is efficient to identify the size of the neighborhood to be considered by the classifier, and also to estimate the weights to be used on the filter.
2. SVM A Support Vector Machine (SVM) is a universal learning machine with a decision surface that is parametrized by a set of support vectors and a corresponding set of weights. The optimal separation of the support vectors from different classes corresponds to the optimal separation of the classes in the complete training set. Given the labeled training set {xi , yi }, with i = 1, 2, . . . , N , yi ∈ {−1, 1} (the labels) and xi ∈
