Second-order Gaussian directional derivative representations for image high-resolution corner detection

TL;DR

This work tackles the problem of accurately detecting adjacent high‑resolution corners by exposing flaws in prior simple corner models and proposing a principled approach based on second‑order Gaussian directional derivatives. It derives SOGDD representations for two high‑resolution corner types (END‑type and L‑type), establishes a scale‑selection framework that ensures corner SOGDD dominates edge SOGDD, and develops a discretized, orientation‑aware detector built on a SODDC matrix with a robust corner metric $\Upsilon$. The method yields a feasible Gaussian scale range $\sigma$ in $(1,1.2)$ and provides a practical pipeline with discretized responses, eigenvalue‑based scoring, and local‑maxima detection. Empirically, it achieves superior localization accuracy, robustness to affine transformations, and strong performance in image matching and 3D reconstruction across multiple datasets, illustrating its practical impact for reliable feature detection and downstream CV tasks.

Abstract

Corner detection is widely used in various computer vision tasks, such as image matching and 3D reconstruction. Our research indicates that there are theoretical flaws in Zhang et al.'s use of a simple corner model to obtain a series of corner characteristics, as the grayscale information of two adjacent corners can affect each other. In order to address the above issues, a second-order Gaussian directional derivative (SOGDD) filter is used in this work to smooth two typical high-resolution angle models (i.e. END-type and L-type models). Then, the SOGDD representations of these two corner models were derived separately, and many characteristics of high-resolution corners were discovered, which enabled us to demonstrate how to select Gaussian filtering scales to obtain intensity variation information from images, accurately depicting adjacent corners. In addition, a new high-resolution corner detection method for images has been proposed for the first time, which can accurately detect adjacent corner points. The experimental results have verified that the proposed method outperforms state-of-the-art methods in terms of localization error, robustness to image blur transformation, image matching, and 3D reconstruction.

Figures (9)

• Figure 1: The results of image corner detection by the SOGDD detector zhang2021corner with different smoothing scales. (a) An image; (b) The results of corner detection by the SOGDD detector zhang2021corner with a given Gaussian smoothing scale ($\sigma^{2}$=2); (c) The results of corner detection by the SOGDD detector zhang2021corner with another Gaussian smoothing scale ($\sigma^{2}$=5); (d) The SOGDD of a corner and an edge point.
• Figure 2: Two common high resolution corner models: (a) END-type high-resolution corner model; (b) L-type high-resolution corner model; $T_1$ and $T_2$ are grayscale values respectively, and two corners are separated by $d$ with $\alpha \in (0, \pi/2)$ and $\beta \in (0, \pi/2)$, $d$ represents the distance between two corners, an edge point locates at $u=d/2$.
• Figure 3: The END-type high-resolution corner model with the SOGDD representations of corner and edge point.
• Figure 4: The L-type high-resolution corner model with the SOGDD representations of corner and edge point.
• Figure 5: Test images (a) ‘Geometric’ and (b) ‘Table’ and their ground truths corner positions.