Related papers: Tropical Geometry Based Edge Detection Using Min-P…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
We present an algorithm for finding a basis of the supereigenvector space in max-plus algebra. The main ideas of the new algorithm are: finding better generators by exploiting the main operation of the tropical double description method and…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
We define a formal framework for the study of algebras of type Max-plus, Min-Plus, tropical algebras, and more generally algebras over a commutative idempotent semi-field. This work is motivated by the increasingly diversified use of these…
Edge detection is one of the most critical tasks in automatic image analysis. There exists no universal edge detection method which works well under all conditions. This paper shows the new approach based on the one of the most efficient…
Edge detection is a cornerstone of image processing, yet existing methods often face critical limitations. Traditional deep learning edge detection methods require extensive training datasets and fine-tuning, while classical techniques…
We present an approach to leaf level segmentation of images of Arabidopsis thaliana plants based upon detected edges. We introduce a novel approach to edge classification, which forms an important part of a method to both count the leaves…
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…
Many edge and contour detection algorithms give a soft-value as an output and the final binary map is commonly obtained by applying an optimal threshold. In this paper, we propose a novel method to detect image contours from the extracted…
The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…
This paper presents an edge detection method based on global and local parameters of the image, which produces satisfactory results on the edge detection of complex images and has a simple structure for execution. The local and global…
Edge Detection Methods Based on Differential Phase Congruency of Monogenic Image Abstract: Edge detection has been widely used in medical image processing and automatic diagnosis. Some novel edge detection algorithms,based on the monogenic…
This paper proposes an unsupervised bottom-up saliency detection approach by aggregating complementary background template with refinement. Feature vectors are extracted from each superpixel to cover regional color, contrast and texture…
In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in…
The tropical semiring is an algebraic system with addition ``$\max$'' and multiplication ``$+$''. As well as in conventional algebra, linear programming in the tropical semiring has been developed. In this study, we introduce a new type of…
We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching…