Related papers: Tropical Geometry Based Edge Detection Using Min-P…
This paper supplements [17], showing that categorically the layered theory is the same as the theory of ordered monoids (e.g. the max-plus algebra) used in tropical mathematics. A layered theory is developed in the context of categories,…
Shape optimization is of great significance in structural engineering, as an efficient geometry leads to better performance of structures. However, the application of gradient-based shape optimization for structural and architectural design…
Recently, Deep-Neural-Network (DNN) based edge prediction is progressing fast. Although the DNN based schemes outperform the traditional edge detectors, they have much higher computational complexity. It could be that the DNN based edge…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backprojection algorithm. In our second method we employ…
Line segment detection plays a cornerstone role in computer vision tasks. Among numerous detection methods that have been recently proposed, the ones based on edge drawing attract increasing attention owing to their excellent detection…
In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…
For tiny obstacle discovery in a monocular image, edge is a fundamental visual element. Nevertheless, because of various reasons, e.g., noise and similar color distribution with background, it is still difficult to detect the edges of tiny…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical multiplicities and a generalization of the Sturmfels-Tevelev…
Existing ocean front detection methods--including histogram-based variance analysis, Lyapunov exponent, gradient thresholding, and machine learning--suffer from critical limitations: discontinuous outputs, over-detection, reliance on…
This paper proposes a new method for horizon detection called the multi-scale cross modal linear feature. This method integrates three different concepts related to the presence of horizon in maritime images to increase the accuracy of…
Based on a description of project networks by max-plus algebra and poset, the adjacency of critical paths is presented using tropical geometry.
In image processing, edge detection is a valuable tool to perform the extraction of features from an image. This detection reduces the amount of information to be processed, since the redundant information (considered less relevant) can be…
We introduce tropical dual numbers as an extension of tropical semiring. By this innovation, one can work with honest ideals, instead of congruences, and recover the Euclidean topology on affine tropical spaces similar to Zariski's approach…
Edge detection is a very essential part of image processing, as quality and accuracy of detection determines the success of further processing. We have developed a new self learning technique for edge detection using dictionary comprised of…
Accurate localization of organ boundaries is critical in medical imaging for segmentation, registration, surgical planning, and radiotherapy. While deep convolutional networks (ConvNets) have advanced general-purpose edge detection to…
We introduce a soft computing approach for automatically selecting and combining indices from remote sensing multispectral images that can be used for classification tasks. The proposed approach is based on a Genetic-Programming (GP)…