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Persistent topology mitigates the excessive freedom of topological equivalence by studying not just a topological space but a filtration of it. This makes it a very effective class of shape descriptors, with an impressive potential for applications in ...

Controlling the construction of geometric objects is important for several Geometric Modeling applications. Homology groups and generators may be useful for this control. For such incremental construction processes, it is interesting to incrementally ...

In this paper, we propose a novel pooling approach for shape classification and recognition using the bag-of-words pipeline, based on topological persistence, a recent tool from Topological Data Analysis. Our technique extends the standard max-pooling, ...

Euclidean rotations in $$\mathbb {R}^n$$Rn are bijective and isometric maps. Nevertheless, they lose these properties when digitized in $$\mathbb {Z}^n$$Zn. For $$n=2$$n=2, the subset of bijective digitized rotations has been described explicitly by ...

A Forman gradient V on a cell complex $$\varGamma $$Γ enables efficient computation of the homology of $$\varGamma $$Γ: the Morse chain complex defined by critical cells of V and their connection through gradient V-paths is equivalent to the homology of ...

In this paper, we propose a method to compute, in parallel, the homology groups of closed meshes i.e., orientable 2D manifolds without boundary represented by combinatorial maps. Our experiments illustrate the interest of our approach which is really ...

Two combinatorial maps $$M_1$$M1 and $$M_2$$M2 overlap if they share a sub-map, called an overlapping pattern, which can be extended without conflicting neither with $$M_1$$M1 nor with $$M_2$$M2. Isomorphism and subisomorphism are two particular cases ...

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for a 2D cubical ...

Can music be represented as a meaningful geometric and topological object? In this paper, we propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the Tonnetz. The Tonnetz is a graph ...

To prevent the release of large quantities of CO$$_{2}$$2 into the atmosphere, carbon capture and storage CCS represents a potential means of mitigating the contribution of fossil fuel emissions to global warming and ocean acidification. Fluvial saline ...

DNA copy number aberrations CNAs play an important role in cancer and can be experimentally detected using microarray comparative genomic hybridization CGH techniques. Amplicons, CNAs that extend over large sections of the genome, are difficult to study ...

Betti numbers are topological invariants that count the number of holes of each dimension in a space. Cubical complexes are a class of CW complex whose cells are cubes of different dimensions such as points, segments, squares, cubes, etc. They are ...

Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in [InlineEquation not available: see fulltext.]. Cohomology and homology groups are well known topological ...

In this paper, a homotopy-based method is employed for the recovery of speech recordings from missing or corrupted samples taken in a noisy environment. The model for the acquisition device is a compressed sensing scenario using Gabor frames. To recover ...

We present a combinatorial algorithm which runs in $$On \log n$$Onlogn time to find largest rectangle LR inside a given digital object without holes, n being the number of pixels on the contour of digital object. The object is imposed on background ...

Shape matching of 3D digital objects is an important domain of study from topological as well as geometric point of view. Shape matching of two or more digital objects by an efficient segmentation-based method is reported in this paper. The method ...

Orthogonal convex skull of a 3D digital object is a maximal volume orthogonal convex polyhedron lying entirely inside the object. An efficient combinatorial algorithm to construct an approximate 3D orthogonal convex skull of a digital object is ...

Voxel carving is a non-invasive and low-cost technique that is used for the reconstruction of a 3D volume from images captured from a set of cameras placed around the object of interest. In this paper we propose a method to topologically analyze a video ...

In this article, we present a novel approach devoted to robustly compute the Reeb graph of a digital binary image, possibly altered by noise. We first employ a skeletonization algorithm, named DECS Discrete Euclidean Connected Skeleton, to calculate a ...

Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions associated with lines ...

The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivated the development of new tools such as persistent homology for exploring ...

This paper discusses the connection between the texture operator LBP local binary pattern and an application of LBPs to persistent homology. A shape representation - the LBP scale space - is defined as a filtration based on the variation of an LBP ...

Discretization of sphere in the integer space follows a particular discretization scheme, which, inï źprinciple, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which ...

Discretized volumes and surfaces--used today in many areas of science and engineering--are approximated from the real objects in a particular theoretical framework. After a discretization produces a triangle mesh 2-manifold surface, a well-formed voxel ...

Given the pairwise distances for a set of unknown points in a known metric space, the distance geometry problem DGP is to compute the point coordinates in conformation with the distance constraints. It is a well-known problem in the Euclidean space, has ...

The goal of this work is to automatically detect and classify a set of geoenvironmental zones of interest in panchromatic aerial images. Focused on a specific area, the zones to be detected are vegetation/mangrove, degradation/desertification, interface ...