相关论文: RGB image-based data analysis via discrete Morse t…

Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…

To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital…

Persistent homology, an algebraic method for discerning structure in abstract data, relies on the construction of a sequence of nested topological spaces known as a filtration. Two-parameter persistent homology allows the analysis of data…

Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…

Image manipulation detection is to identify the authenticity of each pixel in images. One typical approach to uncover manipulation traces is to model image correlations. The previous methods commonly adopt the grids, which are fixed-size…

We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra low signal-to-noise ratio using cubical persistent homology. Our main application is in the identification of atomic columns and other…

Technological development aims to produce generations of increasingly efficient robots able to perform complex tasks. This requires considerable efforts, from the scientific community, to find new algorithms that solve computer vision…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…

Machine learning based malware detection techniques rely on grayscale images of malware and tends to classify malware based on the distribution of textures in graycale images. Albeit the advancement and promising results shown by machine…

Collecting diverse sets of training images for RGB-D semantic image segmentation is not always possible. In particular, when robots need to operate in privacy-sensitive areas like homes, the collection is often limited to a small set of…

Image saliency detection is an active research topic in the community of computer vision and multimedia. Fusing complementary RGB and thermal infrared data has been proven to be effective for image saliency detection. In this paper, we…

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a…

We present a novel discrete optimization-based approach to generate downsampled versions of binary images that are guaranteed to have the same topology as the original, measured by the zeroth and first Betti numbers of the black regions,…

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 cloud obtained from an image, its natural…

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…

Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…

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 existing data structures for simplicial…

We propose a new deep learning architecture for the tasks of semantic segmentation and depth prediction from RGB-D images. We revise the state of art based on the RGB and depth feature fusion, where both modalities are assumed to be…

In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…