Boris Mederos

Surface reconstruction from noisy point clouds

We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demostrate the effectiveness of our algorithm with a number of experimental results.

Moving least squares multiresolution surface approximation

We describe a new method for surface reconstruction based on unorganized point clouds without normals. We also present a new algorithm for refining the initial triangulation. The output of the method is a refined triangular mesh with points on the moving least squares surface of the original point cloud.

Laser scanner super-resolution

We give a method for improving the resolution of surfaces captured with a laser range scanner by combining many very similar scans. This idea is an application of the 2D image processing technique known as superresolution. The input lower-resolution scans are each randomly shifted, so that each one contributes slightly different information to the final model. Noise is reduced by averaging the input scans.

Smooth surface reconstruction from noisy clouds

We describe a new method for surface reconstruction and smoothing based on unorganized noisy point clouds without normals. The output of the method is a refined triangular mesh that approximates the original point cloud while preserving the salient features of the underlying surface. The method has five steps: noise removal, clustering, data reduction, initial reconstruction, and mesh refinement. We also present theoretical justifications for the heuristics used in the reconstruction step.

Noise reduction in small-animal PET images using a multiresolution transform.

In this paper, we address the problem of denoising reconstructed small animal positron emission tomography (PET) images, based on a multiresolution approach which can be implemented with any transform such as contourlet, shearlet, curvelet, and wavelet. The PET images are analyzed and processed in the transform domain by modeling each subband as a set of different regions separated by boundaries. Homogeneous and heterogeneous regions are considered. Each region is independently processed using different filters: a linear estimator for homogeneous regions and a surface polynomial estimator for the heterogeneous region. The boundaries between the different regions are estimated using a modified edge focusing filter. The proposed approach was validated by a series of experiments. Our method achieved an overall reduction of up to 26% in the %STD of the reconstructed image of a small animal NEMA phantom. Additionally, a test on a simulated lesion showed that our method yields better contrast preservation than other state-of-the art techniques used for noise reduction. Thus, the proposed method provides a significant reduction of noise while at the same time preserving contrast and important structures such as lesions.

GP-MPU Method for Implicit Surface Reconstruction

This work addresses the problem of surface reconstruction from unorganized points and normals that are acquired from laser scanning of 3D objects. We propose a novel technique for implicit surface reconstruction that effectively combines the trend setting method known as Multi-level Partition of the Unity (MPU) with the Gaussian Process Regression. The reconstructed implicit surface is obtained by subdividing the domain into a set of smaller sub-domains using the MPU algorithm, in each sub-domain a Gaussian Process Regression is carried out that provides accurate local approximations which are blended to obtain a global representation corresponding to the reconstructed implicit surface. The proposed algorithm is able to deal efficiently with point clouds presenting several features such as complex topology and geometry, missing regions and very low sampling rate. Moreover, we conduct some experiments with several acquired data and perform some comparisons with state of the art techniques showing competitive results.

Similarity kernels for nearest neighbor-based outlier detection

Outlier detection is an important research topic that focuses on detecting abnormal information in data sets and processes. This paper addresses the problem of determining which class of kernels should be used in a geometric framework for nearest neighbor-based outlier detection. It introduces the class of similarity kernels and employs it within that framework. We also propose the use of isotropic stationary kernels for the case of normed input spaces. Two definitions of similarity scores using kernels are given: the k-NN kernel similarity score (kNNSS) and the summation kernel similarity score (SKSS). The paper concludes with preliminary experimental results comparing the performance of kNNSS and SKSS for outlier detection on four data sets. SKSS compared favorably to kNNSS.

Gait recognition from corrupted silhouettes: a robust statistical approach

This paper introduces a method based on robust statistics to build reliable gait signatures from averaging silhouette descriptions, mainly when gait sequences are affected by severe and persistent defects. The term robust refers to the ability of reducing the impact of silhouette defects (outliers) on the average gait pattern, while taking advantage of clean silhouette regions. An extensive experimental framework was defined based on injecting three types of realistic defects (salt and pepper noise, static occlusion, and dynamic occlusion) to clean gait sequences, both separately in an easy setting and jointly in a hard setting. The robust approach was compared against two other operation modes: (1) simple mean (weak baseline) and (2) defect exclusion (strong benchmark). Three gait representation methods based on silhouette averaging were used: Gait Energy Image (GEI), Gradient Histogram Energy Image (GHEI), and the joint use of GEI and HOG descriptors. Quality of gait signatures was assessed by their discriminant power in a large number of gait recognition tasks. Nonparametric statistical tests were applied on recognition results, searching for significant differences between operation modes.

ML-EM reconstruction model including total variation for low dose PET high resolution data

Data acquired through the PET system tend to be very noisy, partly due to low radiation doses. In this paper, a new reconstruction strategy based on a combination of the MLEM and total variation (TV) is presented. A comparision between the MLEM and MLEM-TV algorithms for three numbers of counts were done: (1) at 15 M counts; (2) at 35 M counts; and (3) at 55 M counts. The proposed method MLEM-TV can yield better result for image reconstruction, having a higher ability than the MLEM method to recover the spatial distribution of the counts, at low number of counts. Furthermore, an adaptive regularization parameters are embedded within the method. Experimental results, for the performance evaluation using PET simulated data, demostrate the efficiency of the MLEM-TV reconstruction method proposed, significantly improving the image quality and accuracy from the first iteration of the method, in comparison with that obtained using MLEM. For each reconstruction model under investigation, studies on the effects of image quality were addressed, using the SSIM index. Simulations were addressed using the small mouse MOBY phantom with SimSet.

Regularized implicit surface reconstruction from points and normals

We consider the problem of surface reconstruction of a geometric object from a finite set of sample points with normals. Our contribution is to present a new scheme for implicit surface reconstruction. Similarly to the multilevel partition of unity (MPU) method we hierarchically divide the domain obtaining local approximation for the object on each part, and then patch all together obtaining a global description of the object. Our new scheme uses ridge regression and weighted gradient one fitting techniques to get better stability on local approximations. The method behaves reasonably on sparse set of points and data with holes as those which comes from 3D scanning of real objects.