[Paper Review] Texture Retrieval via the Scattering Transform

Alexander Sagel, Dominik Meyer+1 more|arXiv (Cornell University)|Jan 12, 2015

Image Retrieval and Classification Techniques19 references3 citations

TL;DR

This paper proposes a novel texture retrieval framework using the scattering transform for robust feature extraction, modeling subband coefficients with a Weibull distribution and employing a Bhattacharyya kernel-based similarity measure. The method achieves state-of-the-art retrieval accuracy, particularly excelling with coarse textures and under spatial deformations or blurring.

ABSTRACT

This work studies the problem of content-based image retrieval, specifically, texture retrieval. It focuses on feature extraction and similarity measure for texture images. Our approach employs a recently developed method, the so-called Scattering transform, for the process of feature extraction in texture retrieval. It shares a distinctive property of providing a robust representation, which is stable with respect to spatial deformations. Recent work has demonstrated its capability for texture classification, and hence as a promising candidate for the problem of texture retrieval. Moreover, we adopt a common approach of measuring the similarity of textures by comparing the subband histograms of a filterbank transform. To this end we derive a similarity measure based on the popular Bhattacharyya Kernel. Despite the popularity of describing histograms using parametrized probability density functions, such as the Generalized Gaussian Distribution, it is unfortunately not applicable for describing most of the Scattering transform subbands, due to the complex modulus performed on each one of them. In this work, we propose to use the Weibull distribution to model the Scattering subbands of descendant layers. Our numerical experiments demonstrated the effectiveness of the proposed approach, in comparison with several state of the arts.

Motivation & Objective

• Address the challenge of robust texture retrieval under spatial deformations and noise, which degrade traditional filterbank-based features.
• Develop a statistical model for scattering transform subbands that captures their complex, non-Gaussian distribution, especially due to the modulus operation.
• Design an efficient, low-dimensional feature representation by modeling scattering coefficients with the Weibull distribution to reduce redundancy.
• Introduce a similarity measure based on the Bhattacharyya kernel to compare feature vectors derived from scattering subband histograms.
• Evaluate the method’s performance across diverse texture classes and under degradation (e.g., blurring), demonstrating robustness and generalization.

Proposed method

• Apply the scattering transform (WST) to texture images, generating multi-scale, deformation-stable subband coefficients through wavelet filtering and modulus operations.
• Model the amplitude distribution of each scattering subband using the Weibull distribution, estimated via maximum likelihood (ML) on the subband magnitudes.
• Estimate Weibull parameters (shape k and scale λ) using numerical optimization, with closed-form solutions for λ* in terms of k*.
• Use the Weibull parameters (k*, λ*) as compact, informative features per subband, reducing dimensionality while preserving discriminative power.
• Compute similarity between texture features using the Bhattacharyya kernel, interpreted as an inner product in a Hilbert space, enabling efficient retrieval.
• Construct a CBIR system where query images are processed via WST, features are modeled with Weibull, and similarity is computed via the Bhattacharyya kernel to rank database images.

Experimental results

Research questions

• RQ1 Can the Weibull distribution effectively model the amplitude distribution of scattering transform subbands, especially given the non-Gaussian, complex modulus-induced statistics?
• RQ2 Does modeling scattering subbands with Weibull parameters improve texture retrieval accuracy compared to standard histogram-based methods?
• RQ3 How does the proposed method perform under spatial deformations and image blurring, particularly in comparison to conventional filterbank-based approaches?
• RQ4 Is there a distinction in performance between using regular WST and normalized WST (NWST) coefficients, and if so, for which texture types?
• RQ5 To what extent does the proposed similarity measure based on the Bhattacharyya kernel enhance retrieval performance in a CBIR framework?

Key findings

• The proposed Weibull-based feature modeling outperforms state-of-the-art methods in texture retrieval accuracy, particularly on coarse textures such as Bark0, Bark6, and Terrain10.
• Normalized WST (NWST) achieves superior performance on coarse and uneven textures, while regular WST (WST) performs better on fine structures like Fabric11 and Grass1.
• Under Gaussian blurring, the retrieval performance of WST degrades significantly faster than NWST, confirming that WST relies on fine-scale features vulnerable to smoothing.
• The proposed method maintains high retrieval accuracy even under strong blurring, demonstrating the robustness of the scattering transform's invariance to spatial deformations.
• The Weibull model effectively captures the statistical distribution of scattering subbands, enabling a low-dimensional yet discriminative feature representation with only two parameters per subband.
• The Bhattacharyya kernel-based similarity measure enables efficient and effective comparison of feature vectors, contributing to the overall retrieval performance in the CBIR system.