Contextual Multi-Scale Image Classification on Quadtree
Résumé
In this paper, we propose a novel hierarchical method for remote sensing image classification. The proposed approach integrates an explicit hierarchical graph-based classifier, which uses a quad-tree structure to model multiscale interactions, and a third order Markov mesh random field to deal with pixel wise contextual information in the same scale. The choice of a quad-tree and the third order Markov mesh allow taking benefit from their good analytical properties (especially causality) and consequently apply non-iterative algorithms. Indeed, the Markov mesh is used to incorporate spatial information in each scale of the quad-tree while keeping the causality of the hierarchical model. 1. INTRODUCTION Nowadays, a substantial amount and variety of last-generation high resolution (HR) satellite missions provide images acquired simultaneously at different spatial and spectral resolutions. The main difficulty is to develop a classifier that jointly utilizes the benefits of multi-band and multi-resolution input data while maintaining a good tradeoff between accuracy and computation time. Classification technique as an example of inverse problems can be regarded as the process that estimates hidden information (or latent variables) í µí±¥ (i.e., land cover class labels) from observations í µí±¦ (i.e., satellite data) attached to a set of nodes S. Hence, this problem is ill posed in the sense of Hadamard [1]. The classical way to handle this disadvantage is to regularize the solution by imposing prior knowledge on the labels, which may include, most remarkably, spatial-contextual priors. In this framework, Markov random field (MRF) models are widely used in image classification since they provide a convenient and consistent way of integrating contextual information into the classification scheme [2, 5]. Because of their generally non-causal nature, MRF models for classification lead to iterative inference algorithms that are computationally demanding [6-10]. By contrast, MRF models defined according to hierarchical structures exhibit good methodological and application-oriented properties including causality by using appropriate graphs [11]. Indeed, from a random process perspective, Markovian models show
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