A Saliency-Based Sparse Representation Method for Point Cloud Simplification.

High-resolution 3D scanning devices produce high-density point clouds, which require a large capacity of storage and time-consuming processing algorithms. In order to reduce both needs, it is common to apply surface simplification algorithms as a preprocessing stage. The goal of point cloud simplification algorithms is to reduce the volume of data while preserving the most relevant features of the original point cloud. In this paper, we present a new point cloud feature-preserving simplification algorithm. We use a global approach to detect saliencies on a given point cloud. Our method estimates a feature vector for each point in the cloud. The components of the feature vector are the normal vector coordinates, the point coordinates, and the surface curvature at each point. Feature vectors are used as basis signals to carry out a dictionary learning process, producing a trained dictionary. We perform the corresponding sparse coding process to produce a sparse matrix. To detect the saliencies, the proposed method uses two measures, the first of which takes into account the quantity of nonzero elements in each column vector of the sparse matrix and the second the reconstruction error of each signal. These measures are then combined to produce the final saliency value for each point in the cloud. Next, we proceed with the simplification of the point cloud, guided by the detected saliency and using the saliency values of each point as a dynamic clusterization radius. We validate the proposed method by comparing it with a set of state-of-the-art methods, demonstrating the effectiveness of the simplification method.

Non-Local SVD Denoising of MRI Based on Sparse Representations.

Magnetic Resonance (MR) Imaging is a diagnostic technique that produces noisy images, which must be filtered before processing to prevent diagnostic errors. However, filtering the noise while keeping fine details is a difficult task. This paper presents a method, based on sparse representations and singular value decomposition (SVD), for non-locally denoising MR images. The proposed method prevents blurring, artifacts, and residual noise. Our method is composed of three stages. The first stage divides the image into sub-volumes, to obtain its sparse representation, by using the KSVD algorithm. Then, the global influence of the dictionary atoms is computed to upgrade the dictionary and obtain a better reconstruction of the sub-volumes. In the second stage, based on the sparse representation, the noise-free sub-volume is estimated using a non-local approach and SVD. The noise-free voxel is reconstructed by aggregating the overlapped voxels according to the rarity of the sub-volumes it belongs, which is computed from the global influence of the atoms. The third stage repeats the process using a different sub-volume size for producing a new filtered image, which is averaged with the previously filtered images. The results provided show that our method outperforms several state-of-the-art methods in both simulated and real data.