Wavelet-based segmentation on the sphere

Abstract

Segmentation is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restoration, and many others. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous fields such as cosmology and geophysics. In this work, we propose a wavelet-based method to segment images on the sphere, accounting for the underlying geometry of spherical data. Our method is a direct extension of the tight-frame based segmentation method used to automatically identify tube-like structures such as blood vessels in medical imaging. It is compatible with any arbitrary type of wavelet frame defined on the sphere, such as axisymmetric wavelets, directional wavelets, curvelets, and hybrid wavelet constructions. Such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process. In particular, directional wavelets and curvelets, which were designed to efficiently capture directional signal content, provide additional advantages in segmenting images containing prominent directional and curvilinear features. We present several numerical experiments, applying our wavelet-based segmentation method, as well as the common K-means method, on realworld spherical images, including an Earth topographic map, a light probe image, solar data-sets, and spherical retina images. These experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images, including those with prominent directional features. Moreover, our algorithm is efficient with convergence usually within a few iterations.

Multi-focused image fusion algorithm based on multi-scale hybrid attention residual network

“…On the "Lytro" dataset, we compare our method with those of other representative algorithms. These include the curvilinear wavelet transform (CWT) [54], the dual-channel pulse-coupled neural network (IDCP-CNN) [55], dense SIFT [56], multi-scale weighted gradient (MWG) [57], multi-focus image fusion generative adversarial network (MFIF-GAN) [58], and Squeeze-and-Excitation and Spatial Frequency fusion (SESF-Fuse) [59], as well as Fine-grained Multi-focus Image Fusion (FGMF) [60]. Multi-focus image fusion using structure-guided flow (MFST) [61].…”

Discrete Spherical Image Representation for CNN-Based Inclination Estimation

“…While a conventional camera that captures perspective images originates from the pin-hole camera model, a spherical camera that captures spherical images is represented by the spherical camera model. Spherical images are widely used and have been studied in the fields of medical science, such as representation of the retinal images of the eyes of humans [22], [49], geography, such as representation of the earth [43], meteorology, such as computation of atmospheric motion [42], and computer vision, such as immersive virtual reality [20], [26], [27], visual surveillance [29], augmented reality [25] and robotics [23], [24], [28].…”