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The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…
Image segmentation is an important median level vision topic. Accurate and efficient multiphase segmentation for images with intensity inhomogeneity is still a great challenge. We present a new two-stage multiphase segmentation method…
Topological alignments and snakes are used in image processing, particularly in locating object boundaries. Both of them have their own advantages and limitations. To improve the overall image boundary detection system, we focused on…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Morphological methods play a crucial role in remote sensing image processing, due to their ability to capture and preserve small structural details. However, most of the existing deep learning models for semantic segmentation are based on…
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…
In this paper, we propose a new minimal path model for minimally interactive retinal vessel centerline extraction. The main contribution lies at the construction of a novel coherence-penalized Riemannian metric in a lifted space,…
We propose an attention mechanism for 3D medical image segmentation. The method, named segmentation-by-detection, is a cascade of a detection module followed by a segmentation module. The detection module enables a region of interest to…
Based on a nonlocal Laplacian operator, a novel edge detection method of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge…
Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to…
Rapid and reliable identification of dynamic scene parts, also known as motion segmentation, is a key challenge for mobile sensors. Contemporary RGB camera-based methods rely on modeling camera and scene properties however, are often…
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…
The interactive image segmentation algorithm can provide an intelligent ways to understand the intention of user input. Many interactive methods have the problem of that ask for large number of user input. To efficient produce intuitive…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
In this paper, we propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures via a new deformation estimation…
Image segmentation has long been a basic problem in computer vision. Depth-wise Layering is a kind of segmentation that slices an image in a depth-wise sequence unlike the conventional image segmentation problems dealing with surface-wise…
In recent years, partial differential equation (PDE) systems have been successfully applied to the binarization of text images, achieving promising results. Inspired by the DH model and incorporating a novel image modeling approach, this…
Many geometric machine learning and image analysis applications, require a left-invariant metric on the 5D homogeneous space of 3D positions and orientations SE(3)/SO(2). This is done in Equivariant Neural Networks (G-CNNs), or in PDE-Based…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Image segmentation aims to partition an image according to the objects in the scene and is a fundamental step in analysing very high spatial-resolution (VHR) remote sensing imagery. Current methods struggle to effectively consider land…