Accurate and discernible photocollages

There currently exist several techniques for selecting and combining images from a digital image library into a single image so that the result meets certain prespecified visual criteria. Image mosaic methods, first explored by Connors and Trivedi[18], arrange library images according to some tiling arrangement, often a regular grid, so that the combination of images, when viewed as a whole, resembles some input target image. Other techniques, such as Autocollage of Rother et al.[78], seek only to combine images in an interesting and visually pleasing manner, according to certain composition principles, without attempting to approximate any target image. Each of these techniques provide a myriad of creative options for artists who wish to combine several levels of meaning into a single image or who wish to exploit the meaning and symbolism contained in each of a large set of images through an efficient and easy process. We first examine the most notable and successful of these methods, and summarize the advantages and limitations of each. We then formulate a set of goals for an image collage system that combines the advantages of these methods while addressing and mitigating the drawbacks. Particularly, we propose a system for creating photocollages that approximate a target image as an aggregation of smaller images, chosen from a large library, so that interesting visual correspondences between images are exploited. In this way, we allow users to create collages in which multiple layers of meaning are encoded, with meaningful visual links between each layer. In service of this goal, we ensure that the images used are as large as possible and are combined in such a way that boundaries between images are not immediately apparent, as in Autocollage. This has required us to apply a multiscale approach to searching and comparing images from a large database, which achieves both speed and accuracy. We also propose a new framework for color post-processing, and propose novel techniques for decomposing images according to object and texture information

Differentiable Surface Triangulation

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably perturbed weighted Delaunay triangulation. We translate this result into a computational algorithm by proposing a soft relaxation of the classical weighted Delaunay triangulation and optimizing over vertex weights and vertex locations. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints. We demonstrate the efficacy of our method on various planar and surface meshes on a range of difficult-to-optimize objective functions. Our code can be found online: https://github.com/mrakotosaon/diff-surface-triangulation

Analysis and Generation of Quality Polytopal Meshes with Applications to the Virtual Element Method

This thesis explores the concept of the quality of a mesh, the latter being intended as the discretization of a two- or three- dimensional domain. The topic is interdisciplinary in nature, as meshes are massively used in several fields from both the geometry processing and the numerical analysis communities. The goal is to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. In other words, a good quality mesh that is also cheap to handle, overcoming the typical trade-off between quality and computational cost. To reach this goal, we first need to answer the question: ''How, and how much, does the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depend on the particular mesh adopted to model the problem? And which geometrical features of the mesh most influence the result?'' We present a comparative study of the different mesh types, mesh generation techniques, and mesh quality measures currently available in the literature related to both engineering and computer graphics applications. This analysis leads to the precise definition of the notion of quality for a mesh, in the particular context of numerical simulations of partial differential equations with the virtual element method, and the consequent construction of criteria to determine and optimize the quality of a given mesh. Our main contribution consists in a new mesh quality indicator for polytopal meshes, able to predict the performance of the virtual element method over a particular mesh before running the simulation. Strictly related to this, we also define a quality agglomeration algorithm that optimizes the quality of a mesh by wisely agglomerating groups of neighboring elements. The accuracy and the reliability of both tools are thoroughly verified in a series of tests in different scenarios

Detection algorithms for spatial data

This dissertation addresses the problem of anomaly detection in spatial data. The problem of landmine detection in airborne spatial data is chosen as the specific detection scenario. The first part of the dissertation deals with the development of a fast algorithm for kernel-based non-linear anomaly detection in the airborne spatial data. The original Kernel RX algorithm, proposed by Kwon et al. [2005a], suffers from the problem of high computational complexity, and has seen limited application. With the aim to reduce the computational complexity, a reformulated version of the Kernel RX, termed the Spatially Weighted Kernel RX (SW-KRX), is presented. It is shown that under this reformulation, the detector statistics can be obtained directly as a function of the centered kernel Gram matrix. Subsequently, a methodology for the fast computation of the centered kernel Gram matrix is proposed. The key idea behind the proposed methodology is to decompose the set of image pixels into clusters, and expediting the computations by approximating the effect of each cluster as a whole. The SW-KRX algorithm is implemented for a special case, and comparative results are compiled for the SW-KRX vis-à-vis the RX anomaly detector. In the second part of the dissertation, a detection methodology for buried mine detection is presented. The methodology is based on extraction of color texture information using cross-co-occurrence features. A feature selection methodology based on Bhattacharya coefficients and principal feature analysis is proposed and detection results with different feature-based detectors are presented, to demonstrate the effectiveness of the proposed methodology in the extraction of useful discriminatory information --Abstract, page iii

Waterpixels

International audience— Many approaches for image segmentation rely on a 1 first low-level segmentation step, where an image is partitioned 2 into homogeneous regions with enforced regularity and adherence 3 to object boundaries. Methods to generate these superpixels have 4 gained substantial interest in the last few years, but only a few 5 have made it into applications in practice, in particular because 6 the requirements on the processing time are essential but are not 7 met by most of them. Here, we propose waterpixels as a general 8 strategy for generating superpixels which relies on the marker 9 controlled watershed transformation. We introduce a spatially 10 regularized gradient to achieve a tunable tradeoff between the 11 superpixel regularity and the adherence to object boundaries. 12 The complexity of the resulting methods is linear with respect 13 to the number of image pixels. We quantitatively evaluate our 14 approach on the Berkeley segmentation database and compare 15 it against the state-of-the-art