Multiscale Corner Detection in Planar Shapes

Abstract

This paper presents a multiscale corner detection method in planar shapes, which applies an undecimated Mexican hat wavelet decomposition of the angulation signal to identify significant points on a shape contour. The advantage of using this wavelet is that it is well suited for detecting singularities as corners and contours due to its excellent selectivity in position. Thus, this wavelet plays an important role in our approach because it identifies changes in non-stationary angulation signals, and it can be extended to multidimensional approaches in an efficient way when approximating this wavelet by difference of Gaussian. The proposed algorithm detects peaks on a correlation signal which is generated from different wavelet scales and retains relevant points on the decomposed angulation signal while discards poor information. Our approach assumes that only peaks which persist through several scales correspond to corners. Furthermore, we introduce a novel procedure to tune parameters for the corner detection algorithms that corresponds to the best relation between Precision and Recall measures. This technique guides the parameter adjustment of the algorithms according to the image database and it improves their performance with regard to true corner detection. Concerning the performance assessment of the algorithms, we compare the proposed one to other corner detectors by using Precision and Recall measures which are based on ground-truth information. Tests were carried out using more than a hundred images from a non-homogenous database that contains noisy and non-noisy binary shapes 1

Shape retrieval by corners and Dynamic Space Warping

“…Our methodology employs a multi-scale algorithm for corner detection introduced in [14]. The corner detector requires the parameterized shape contour Γ(t) = (x(t), y(t)), where x and y correspond to the coordinates of all t points which belong to the contour.…”

“…The differences among these representations constitute the detail coefficients of this wavelet decomposition. In fact, the approach we have employed for corner detection was introduced by Paula et al [14]. It performs an interscale correlation and from this direct spatial correlation between adjacent scales the algorithm evaluates the detail coefficients.…”

A multiscale shape descriptor based on diferential entropy

“…Shape analysis and recognition tasks can benefit from algorithms that use multiscale curvature to represent the shapes of objects (Paula et al, 2013;Souza et al, 2016;Carneiro et al, 2017) or monoscale description (Ushizima et al, 2015). Shape representation can also be performed to handle corners in tasks such as scene analysis, polygonal…”

“…approximation, feature matching, robot navigation, shape similarity and object tracking, to name only a few (Paula et al, 2013). Souza et al (2016) designed a new approach to optimising the parameters of the normalised multiscale bending energy (NMBE) (Cesar Jr and Costa, 1997) in order to improve its shape discrimination ability.…”

Laplacian Scale-Space Behavior of Planar Curve Corners

“…The DCSS computes the curvature of the planar curve byφ(s) whereas the CSS by [ẋ(s)ÿ(s)−ẍ(s)ẏ(s)]/[(ẋ(s) 2 +ẏ(s) 2 )] 3/2 . There are also many scale-space corner detectors based on other measures [30] [31] [22] [24] [32]. As far as we know, none of this corner detection research analyzes scale-space behavior.…”