Digital Image Processing Techniques
50 papers on this topic
Pitfalls of topology-aware image segmentation
Topological correctness, i.e., the preservation of structural integrity and specific characteristics of shape, is a fundamental requirement for medical imaging tasks, such as neuron or vessel...
Matrix-Valued LogSumExp Approximation for Colour Morphology
Mathematical morphology is a part of image processing that uses a window that moves across the image to change certain pixels according to certain operations. The concepts of supremum and infimum...
Hadamard Row-Wise Generation Algorithm
In this paper, we introduce an efficient algorithm for generating specific Hadamard rows, addressing the memory demands of pre-computing the entire matrix. Leveraging Sylvester's recursive...
Effective data reduction algorithm for topological data analysis
One of the most interesting tools that have recently entered the data science toolbox is topological data analysis (TDA). With the explosion of available data sizes and dimensions, identifying and...
A Discrete Scheme for Computing Image's Weighted Gaussian Curvature
Weighted Gaussian Curvature is an important measurement for images. However, its conventional computation scheme has low performance, low accuracy and requires that the input image must be second...
A Topological "Reading" Lesson: Classification of MNIST using TDA
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point...
Component Tree Loss Function: Definition and Optimization
In this article, we propose a method to design loss functions based on component trees which can be optimized by gradient descent algorithms and which are therefore usable in conjunction with...
Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure
Mathematical morphology (MM) is a theory of non-linear operators used for the processing and analysis of images. Morphological neural networks (MNNs) are neural networks whose neurons compute...
A New Clustering Method Based on Morphological Operations
With the booming development of data science, many clustering methods have been proposed. All clustering methods have inherent merits and deficiencies. Therefore, they are only capable of...
Appearance Shock Grammar for Fast Medial Axis Extraction from Real Images
We combine ideas from shock graph theory with more recent appearance-based methods for medial axis extraction from complex natural scenes, improving upon the present best unsupervised method, in...
Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be...
Tropical Geometry and Piecewise-Linear Approximation of Curves and Surfaces on Weighted Lattices
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...
RecurSIA-RRT: Recursive translatable point-set pattern discovery with removal of redundant translators
We introduce two algorithms, RECURSIA and RRT, designed to increase the compression factor achievable using point-set cover algorithms based on the SIA and SIATEC pattern discovery algorithms. SIA...
Computing discrete Morse complexes from simplicial complexes
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze...
Challenges in Reconstructing Shapes from Euler Characteristic Curves
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and...
Graph Reconstruction by Discrete Morse Theory
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a...
Detection and skeletonization of single neurons and tracer injections using topological methods
Neuroscientific data analysis has traditionally relied on linear algebra and stochastic process theory. However, the tree-like shapes of neurons cannot be described easily as points in a vector...
Descriptive Unions. A Fibre Bundle Characterization of the Union of Descriptively Near Sets
This paper introduces an extension of descriptive intersection and provides a framework for descriptive unions of nonempty sets. Fibre bundles provide structures that characterize spatially near...