Stable and Invertible Generic Fourier Descriptors for Shape-Based Image Classification

The increasing consumer demand for smart surveillance devices capable of behavior analysis and danger alerting has led to the utilization of various descriptors for image recognition across applications, independent of image position, orientation, and scale. Despite this, few studies have focused on the completeness property of invariant descriptors for grayscale, color, and three-dimensional images. Completeness ensures descriptor distinctiveness for specific shapes, a property that is challenging to achieve and, at times, has been accessible for planar curves. The recently introduced concept of invariants’ invertibility, associated with completeness, facilitates the reconstruction of an object’s shape through similar transformations. This paper proposes a Stable and Invertible Generic Fourier Descriptor (SIGFD) for gray-level images. We demonstrate the invariance, convergence, and completeness properties of the proposed SIGFD set. To assess its robustness, we conduct experimental evaluations on well-known datasets such as Kimia 99, MPEG-7, and COIL100. Additionally, we utilize our proprietary FSTEF Faces dataset to further evaluate face recognition performance. The effectiveness of the proposed SIGFD sets is evidenced through the various studies presented in this work.