RSD-DOG : A New Image Descriptor based on Second Order Derivatives

TL;DR

RSD-DOG introduces a compact second-order image patch descriptor that captures ridges and valleys by combining rotating directional filters with Difference of Gaussian. By treating image patches as 3D surfaces and binning orientations derived from DHSF-driven ridge/valley directions, it achieves a 256-dimensional descriptor with strong illumination, rotation, scale, blur, and viewpoint robustness. Evaluations on the Oxford dataset show that RSD-DOG outperforms SIFT, GLOH, DAISY, GIST, and LIDRIC, especially under complex illumination changes, while offering significantly lower dimensionality than typical second-order descriptors. The work suggests potential extensions to learning-based parameter optimization and parallel implementations for faster descriptor generation, broadening applicability to image matching, retrieval, and recognition.

Abstract

This paper introduces the new and powerful image patch descriptor based on second order image statistics/derivatives. Here, the image patch is treated as a 3D surface with intensity being the 3rd dimension. The considered 3D surface has a rich set of second order features/statistics such as ridges, valleys, cliffs and so on, that can be easily captured by using the difference of rotating semi Gaussian filters. The originality of this method is based on successfully combining the response of the directional filters with that of the Difference of Gaussian (DOG) approach. The obtained descriptor shows a good discriminative power when dealing with the variations in illumination, scale, rotation, blur, viewpoint and compression. The experiments on image matching, demonstrates the advantage of the obtained descriptor when compared to its first order counterparts such as SIFT, DAISY, GLOH, GIST and LIDRIC.

Figures (9)

• Figure 1: (a) Image representation in 2D. (b) and (c) The same image being represented in 3D, with intensity being the third dimension. Both (b) and (c) when viewed from different angles, exhibits a set of second order statistics such as ridges, valleys, summits, edges etc.
• Figure 2: A smoothing rotating filter and Difference of Half smoothing Filters (DHSF). For (d) top: $\mu = 10$ and $\lambda = 1$. For (d) bottom: $\mu = 10$ and $\lambda = 1.5$.
• Figure 3: DHSF filter descriptions.
• Figure 4: Points selection on a synthetic image. Examples of functions $D(x,y,\theta)$ on the points selected on synthetic image using $\mu = 10, \lambda_1 = 1, \lambda_2 = 1.5$. The x-axis corresponds to the value of $\theta$ (in degrees) and the y-axis to $D(x,y,\theta)$.
• Figure 5: Methodology involved in the construction of RSD-DOG descriptor.