Related papers: Generating minimal boundary maps
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…
We compare various viewpoints on down-sets (simplicial complexes), illustrating how the combinatorial inclusion-exclusion principle may serve as an alternative to more advanced methods of studying their face numbers.
We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial $Q_g^n(x)$ where $x$ is a parameter taking the number of…
We propose a method for constructing generative models of 3D objects from a single 3D mesh and improving them through unsupervised low-shot learning from 2D images. Our method produces a 3D morphable model that represents shape and albedo…
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
Generative DNNs are a powerful tool for image synthesis, but they are limited by their computational load. On the other hand, given a trained model and a task, e.g. faces generation within a range of characteristics, the output image…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
The perception of high-definition maps is an integral component of environmental perception in autonomous driving systems. Existing research have often focused on online construction of high-definition maps. For instance, the Maptr[9]…
In agent-based simulations, synthetic populations of agents are commonly used to represent the structure, behaviour, and interactions of individuals. However, generating a synthetic population that accurately reflects real population…
In this paper we present a technique for procedurally generating 3D maps using a set of premade meshes which snap together based on designer-specified visual constraints. The proposed approach avoids size and layout limitations, offering…
Text-to-image models are powerful tools for image creation. However, the generation process is akin to a dice roll and makes it difficult to achieve a single image that captures everything a user wants. In this paper, we propose a framework…
We employ projective Fra\"iss\'e theory to define the "generic combinatorial $n$-simplex" as the pro-finite, simplicial complex that is canonically associated with a family of simply defined selection maps between finite triangulations of…
To generate new images for a given category, most deep generative models require abundant training images from this category, which are often too expensive to acquire. To achieve the goal of generation based on only a few images, we propose…
A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
In this paper, an adversarial architecture for facial depth map estimation from monocular intensity images is presented. By following an image-to-image approach, we combine the advantages of supervised learning and adversarial training,…