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We introduce a Lennard-Jones layer (LJL) to equalize the density across the distribution of 2D and 3D point clouds by systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by solely considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution over the 2D Euclidean plane and 3D mesh surfaces. Moreover, LJLs are embedded in point cloud generative network architectures by adding them at later stages of the inference process. The improvements coming with LJLs for generating 3D point clouds are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural networks.

[pt] A aquisição de malhas triangulares normalmente introduz ruídos indesejados. A remoção de ruído de malhas é uma tarefa da área de processamento geométrico que serve para remover esse tipo de distorção. Para preservar a fidelidade em relação à malha desejada, um algoritmo de remoção de ruído de malha deve preservar detalhes enquanto remove altas frequências indesejadas sobre a superfície. Vários algoritmos foram propostos para resolver este problema usando um esquema de filtragem bilateral. Neste trabalho, propomos um algoritmo de dois passos que usa vizinhança adaptativa e filtragem bilateral para remover ruído do campo normal e, em seguida, atualizar as posições dos vértices ajustando os triângulos às novas normais. A nossa contribuição principal é a computação da vizinhança adaptativa. Essa computação é formulada como problemas locais de otimização quadrática que podem ser controlados para obter o comportamento desejado da vizinhança. A proposta é comparada visual e quantitativamente com vários algoritmos propostos na literatura, usando dados sintéticos e reais. / [en] The acquisition of triangular meshes typically introduces undesired noise. Mesh denoising is a geometry processing task to remove this kind of distortion. To preserve the geometric fidelity of the desired mesh, a mesh denoising algorithm must preserve true details while removing artificial high-frequencies from the surface. Several algorithms were proposed to address this problem using a bilateral filtering scheme. In this work, we propose a two-step algorithm which uses adaptive patches and bilateral filtering to denoise the normal field, and then update vertex positions fitting the faces to the denoised normals. The computation of the adaptive patches is our main contribution. We formulate this computation as local quadratic optimization problems that we can control to obtain a desired behavior of the patch. We compared our proposal with several algorithms proposed in the literature using synthetic and real data.

Yes / The development of the patchwise Partial Di erential Equation (PDE) framework a few years a- go has paved the way for the PDE method to be used in mesh signal processing. In this paper we, for the rst time, extend the use of the PDE method to progressive mesh compression and mesh denoising. We, meanwhile, upgrade the existing patchwise PDE method in patch merging, mesh partitioning, and boundary extraction to accommodate mesh signal processing. In our new method an arbitrary mesh model is partitioned into patches, each of which can be represented by a small set of coe cients of its PDE spectral solution. Since low- frequency components contribute more to the recon- structed mesh than high-frequency ones, we can achieve progressive mesh compression and mesh denoising by manipulating the frequency terms of the PDE solution. Experimental results demonstrate the feasibility of our method in both progressive mesh compression and mesh denoising.

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We propose a method of adaptive image denoising using a support vector machine (SVM) classifier to select between multiple well-performing contemporary denoising algorithms for each pixel of a noisy image. We begin by proposing a simple method for realistically generating noisy images, and also describe a number of novel and pre-existing features based on seam energy, local colour, and saliency which are used as classifier inputs. Our SVM strategic image denoising (SVMSID) results demonstrate better image quality than either candidate denoising algorithm for images of moderate noise level, as measured using the perceptually-based quaternion structural similarity image metric (QSSIM). We also demonstrate a modified training point selection method to improve robustness across many noise levels, and propose various extensions to SVMSID for further exploration. / Thesis / Master of Applied Science (MASc)

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Scientific visualization is an essential and indispensable tool for the systematic study of computational (CFD) datasets. There are numerous methods currently used for the unwieldy task of processing and visualizing the characteristically large datasets. Feature extraction is one such technique and has become a significant means for enabling effective visualization. This thesis proposes different modules to refine the maps which are generated from a feature detection on a dataset. The specific example considered in this work is the vortical flow in a two-dimensional oceanographic dataset. This thesis focuses on performing feature extraction by detecting the features and processing the feature maps in three different modules, namely, denoising, segmenting and ranking. The denoising module exploits a wavelet-based multiresolution analysis (MRA). Although developed for two-dimensional datasets, these techniques are directly extendable to three-dimensional cases. A comparative study of the performance of Optimal Feature-Preserving (OFP) filters and non-OFP filters for denoising is presented. A computationally economical implementation for segmenting the feature maps as well as different algorithms for ranking the regions of interest (ROI's) are also discussed in this work.

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