Abstract
Wavelet Packets (WPs) bases are explored seeking new discriminative features for texture indexing. The task of WP feature design is formulated as a learning decision problem by selecting the filter-bank structure of a basis (within a WPs family) that offers an optimal balance between estimation and approximation errors. To address this problem, a computationally efficient algorithm is adopted that uses the tree-structure of the WPs collection and the Kullback-Leibler divergence as a discrimination criterion. The adaptive nature of the proposed solution is demonstrated in synthetic and real data scenarios. With synthetic data, we demonstrate that the proposed features can identify discriminative bands, which is not possible with standard wavelet decomposition. With data with real textures, we show performance improvements with respect to the conventional Wavelet-based decomposition used under the same conditions and model assumptions.
Highlights
In the current information age, we have access to unprecedented sources of digital image content
We revisit the statistical framework in [4] to include a family of transform-based representations of the image space with a non-uniform number of transform coefficients per sub-band, and within this context, we introduce Wavelet Packets (WPs) for texture retrieval
We show that basis selection (BS) is equivalent to a minimum costtree pruning problem with natural connections with the type of minimum cost-tree pruning algorithms used in classification and regression trees (CART) [48]
Summary
In the current information age, we have access to unprecedented sources of digital image content. Being able to index and organize these documents based solely on the content extracted from the signals without relying on metadata or expensive human annotations has become a central problem [1]–[21] In this context, an important task in image processing is texture retrieval. For the FE stage, the Wavelet transform (WT) has been widely adopted as a tool to decompose and organize the signal content in sub-spaces associated with different levels of resolution (or scale) information [30], [31] Based on this sub-space decomposition, energy features have been used as a signature that represents the salient texture attributes for texture indexing [32]. We can construct a rich collection of sub-space decompositions of the image space by iterating the TCF in different bands [31], gaining access to information from different layers in the context of the convolution-based network of representations that is used to create WPs bases [30], [31].This rich spacescale family of decompositions of the image space (organized in a network of quad-trees) can be used to find new convolutional-based features that could be more effective for texture discrimination, and new representations that can be adapted to the task (i.e., learned from some available data)
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