Related papers: Branched Signature Model
Normal map is an important and efficient way to represent complex 3D models. A designer may benefit from the auto-generation of high quality and accurate normal maps from freehand sketches in 3D content creation. This paper proposes a deep…
In this paper we generalize special geometry to arbitrary signatures in target space. We formulate the definitions in a precise mathematical setting and give a translation to the coordinate formalism used in physics. For the projective…
Current successful approaches for generic (non-semantic) segmentation rely mostly on edge detection and have leveraged the strengths of deep learning mainly by improving the edge detection stage in the algorithmic pipeline. This is in…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…
Motivation of our work is to present a new methodology for symbol recognition. We support structural methods for representing visual associations in graphic documents. The proposed method employs a structural approach for symbol…
We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns closely with the notions of tree-depth and shrub-depth of graphs…
We prove that a continuous path with finite length in a real Banach space cannot have infinitely many zero components in its signature unless it is tree-like. In particular, this allows us to strengthen a limit theorem for signature…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…
Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little…
A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
In this work, we relate girth and path-degeneracy in classes with sub-exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor-closed classes that are tight up to a constant factor (and tight up to…
Detection of curvilinear structures in images has long been of interest. One of the most challenging aspects of this problem is inferring the graph representation of the curvilinear network. Most existing delineation approaches first…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
A bounded curvature path is a continuously differentiable piece-wise $C^2$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and…
Signed networks, characterized by edges labeled as either positive or negative, offer nuanced insights into interaction dynamics beyond the capabilities of unsigned graphs. Central to this is the task of identifying the maximum balanced…
William Thurston (1946-2012) gave a combinatorial characterization for generic branched self-coverings of the two-sphere by associating a planar graph to them 10.48550/arXiv.1502.04760. By generalizing the notion of local balancing, the…