Related papers: Geometric Shape Features Extraction Using a Steady…
This paper presents a mathematical analysis of an elliptic partial differential equation (PDE) designed to compute the geometric thickness of a given shape. The PDE-based formulation provides a direct and systematic approach to evaluate…
Partial differential equations can be used for extracting geometric features of shapes. This article summarizes recent methods to extract the normal vector field from an elliptic equation proposed by Yamada and from the heat equation, and…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
We demonstrate the use of similarity domains (SDs) for shape modeling and skeleton extraction. SDs are recently proposed and they can be utilized in a neural network framework to help us analyze shapes. SDs are modeled with radial basis…
This paper describes a geometry based technique for feature extraction applicable to segmentation-based word recognition systems. The proposed system extracts the geometric features of the character contour. This features are based on the…
In this paper, a feature extraction approach for the deformable linear object is presented, which uses a Bezier curve to represent the original geometric shape. The proposed extraction strategy is combined with a parameterization technique,…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
This study introduces a novel unsupervised medical image feature extraction method that employs spatial stratification techniques. An objective function based on weight is proposed to achieve the purpose of fast image recognition. The…
The same type of objects in different images may vary in their shapes because of rigid and non-rigid shape deformations, occluding foreground as well as cluttered background. The problem concerned in this work is the shape extraction in…
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…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…
How to effectively remove the noise while preserving the image structure features is a challenging issue in the field of image denoising. In recent years, fractional PDE based methods have attracted more and more research efforts due to the…
Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objects are segmented, selective segmentation is used to isolate specific objects in an image and is of particular…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
This paper introduces a novel partial differential equation (PDE) framework for single-image dehazing. We embed the atmospheric scattering model into a PDE featuring edge-preserving diffusion and a nonlocal operator to maintain both local…