A Volumetric Approach to Point Cloud Compression, Part II: Geometry Compression.

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Attribute compression is addressed in Part I of this paper, while geometry compression is addressed in Part II. Geometry is represented implicitly as the level set of a volumetric function (the signed distance function or similar). Experimental results show that geometry compression using volumetric functions improves over the methods used in the emerging MPEG Point Cloud Compression (G-PCC) standard.

A Volumetric Approach to Point Cloud Compression, Part I: Attribute Compression.

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Geometry compression is addressed in Part II of this paper, while attribute compression is addressed in Part I. Attributes are represented by a volumetric function whose coefficients can be regarded as a critically sampled orthonormal transform that generalizes the recent successful region-adaptive hierarchical (or Haar) transform to higher orders. Experimental results show that attribute compression using higher order volumetric functions is an improvement over the first order functions used in the emerging MPEG Point Cloud Compression standard.

Compression of Plenoptic Point Clouds.

Point clouds have been recently used in applications involving real-time capture and rendering of 3D objects. In a point cloud, for practical reasons, each point or voxel is usually associated with one single color along with other attributes. The region-adaptive hierarchical transform (RAHT) coder has been proposed for single-color point clouds. The cloud is usually captured by many cameras and the colors are averaged in some fashion to yield the point color. This approach may not be very realistic since, in real world objects, the reflected light may significantly change with the viewing angle, especially if specular surfaces are present. For that, we are interested in a more complete representation, the plenoptic point cloud, wherein every point has associated colors in all directions. Here, we propose a compression method for such a representation. Instead of encoding a continuous function, since there is only a finite number of cameras, it makes sense to compress as many colors per voxel as cameras, and to leave any intermediary color rendering interpolation to the decoder. Hence, each voxel is associated with a vector of color values, for each color component. We have here developed and evaluated four methods to expand the RAHT coder to encompass the multiple colors case. Experiments with synthetic data helped us to correlate specularity with the compression, since object specularity, at a given point in space, directly affects color disparity among the cameras, impacting the coder performance. Simulations were carried out using natural (captured) data and results are presented as rate-distortion curves that show that a combination of Kahunen-Loève transform and RAHT achieves the best performance.

Transform Coding for Point Clouds Using a Gaussian Process Model.

We propose using stationary Gaussian processes (GPs) to model the statistics of the signal on points in a point cloud, which can be considered samples of a GP at the positions of the points. Furthermore, we propose using Gaussian process transforms (GPTs), which are Karhunen-Loève transforms of the GP, as the basis of transform coding of the signal. Focusing on colored 3D point clouds, we propose a transform coder that breaks the point cloud into blocks, transforms the blocks using GPTs, and entropy codes the quantized coefficients. The GPT for each block is derived from both the covariance function of the GP and the locations of the points in the block, which are separately encoded. The covariance function of the GP is parameterized, and its parameters are sent as side information. The quantized coefficients are sorted by the eigenvalues of the GPTs, binned, and encoded using an arithmetic coder with bin-dependent Laplacian models, whose parameters are also sent as side information. Results indicate that transform coding of 3D point cloud colors using the proposed GPT and entropy coding achieves superior compression performance on most of our data sets.

Motion-Compensated Compression of Dynamic Voxelized Point Clouds.

Dynamic point clouds are a potential new frontier in visual communication systems. A few articles have addressed the compression of point clouds, but very few references exist on exploring temporal redundancies. This paper presents a novel motion-compensated approach to encoding dynamic voxelized point clouds at low bit rates. A simple coder breaks the voxelized point cloud at each frame into blocks of voxels. Each block is either encoded in intra-frame mode or is replaced by a motion-compensated version of a block in the previous frame. The decision is optimized in a rate-distortion sense. In this way, both the geometry and the color are encoded with distortion, allowing for reduced bit-rates. In-loop filtering is employed to minimize compression artifacts caused by distortion in the geometry information. Simulations reveal that this simple motion-compensated coder can efficiently extend the compression range of dynamic voxelized point clouds to rates below what intra-frame coding alone can accommodate, trading rate for geometry accuracy.

Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform.

In free-viewpoint video, there is a recent trend to represent scene objects as solids rather than using multiple depth maps. Point clouds have been used in computer graphics for a long time, and with the recent possibility of real-time capturing and rendering, point clouds have been favored over meshes in order to save computation. Each point in the cloud is associated with its 3D position and its color. We devise a method to compress the colors in point clouds, which is based on a hierarchical transform and arithmetic coding. The transform is a hierarchical sub-band transform that resembles an adaptive variation of a Haar wavelet. The arithmetic encoding of the coefficients assumes Laplace distributions, one per sub-band. The Laplace parameter for each distribution is transmitted to the decoder using a custom method. The geometry of the point cloud is encoded using the well-established octtree scanning. Results show that the proposed solution performs comparably with the current state-of-the-art, while being much more computationally efficient. We believe this paper represents the state of the art in intra-frame compression of point clouds for real-time 3D video.

Graph-Based Compression of Dynamic 3D Point Cloud Sequences.

This paper addresses the problem of compression of 3D point cloud sequences that are characterized by moving 3D positions and color attributes. As temporally successive point cloud frames share some similarities, motion estimation is key to effective compression of these sequences. It, however, remains a challenging problem as the point cloud frames have varying numbers of points without explicit correspondence information. We represent the time-varying geometry of these sequences with a set of graphs, and consider 3D positions and color attributes of the point clouds as signals on the vertices of the graphs. We then cast motion estimation as a feature-matching problem between successive graphs. The motion is estimated on a sparse set of representative vertices using new spectral graph wavelet descriptors. A dense motion field is eventually interpolated by solving a graph-based regularization problem. The estimated motion is finally used for removing the temporal redundancy in the predictive coding of the 3D positions and the color characteristics of the point cloud sequences. Experimental results demonstrate that our method is able to accurately estimate the motion between consecutive frames. Moreover, motion estimation is shown to bring a significant improvement in terms of the overall compression performance of the sequence. To the best of our knowledge, this is the first paper that exploits both the spatial correlation inside each frame (through the graph) and the temporal correlation between the frames (through the motion estimation) to compress the color and the geometry of 3D point cloud sequences in an efficient way.

Automated detection of whole-cell mitochondrial motility and its dependence on cytoarchitectural integrity.

Current methodologies used for mitochondrial motility analysis tend to either overlook individual mitochondrial tracks or analyze only peripheral mitochondria instead of mitochondria in all regions of the cell. Furthermore, motility analysis of an individual mitochondrion is usually quantified by establishing an arbitrary threshold for "directed" motion. In this work, we created a custom, publicly available computational algorithm based on a previously published approach (Giedt et al., 2012. Ann Biomed Eng 40:1903-1916) in order to characterize the distribution of mitochondrial movements at the whole-cell level, while still preserving information about single mitochondria. Our technique is easy to use, robust, and computationally inexpensive. Images are first pre-processed for increased resolution, and then individual mitochondria are tracked based on object connectivity in space and time. When our method is applied to microscopy fields encompassing entire cells, we reveal that the mitochondrial net distances in fibroblasts follow a lognormal distribution within a given cell or group of cells. The ability to model whole-cell mitochondrial motility as a lognormal distribution provides a new quantitative paradigm for comparing mitochondrial motility in naïve and treated cells. We further demonstrate that microtubule and microfilament depolymerization shift the lognormal distribution in directions which indicate decreased and increased mitochondrial movement, respectively. These findings advance earlier work on neuronal axons (Morris and Hollenbeck, 1993. J Cell Sci 104:917-927) by relating them to a different cell type, applying them on a global scale, and automating measurement of mitochondrial motility in general.

Rate-constrained 3D surface estimation from noise-corrupted multiview depth videos.

Transmitting compactly represented geometry of a dynamic 3D scene from a sender can enable a multitude of imaging functionalities at a receiver, such as synthesis of virtual images at freely chosen viewpoints via depth-image-based rendering. While depth maps­projections of 3D geometry onto 2D image planes at chosen camera viewpoints-can nowadays be readily captured by inexpensive depth sensors, they are often corrupted by non-negligible acquisition noise. Given depth maps need to be denoised and compressed at the encoder for efficient network transmission to the decoder, in this paper, we consider the denoising and compression problems jointly, arguing that doing so will result in a better overall performance than the alternative of solving the two problems separately in two stages. Specifically, we formulate a rate-constrained estimation problem, where given a set of observed noise-corrupted depth maps, the most probable (maximum a posteriori (MAP)) 3D surface is sought within a search space of surfaces with representation size no larger than a prespecified rate constraint. Our rate-constrained MAP solution reduces to the conventional unconstrained MAP 3D surface reconstruction solution if the rate constraint is loose. To solve our posed rate-constrained estimation problem, we propose an iterative algorithm, where in each iteration the structure (object boundaries) and the texture (surfaces within the object boundaries) of the depth maps are optimized alternately. Using the MVC codec for compression of multiview depth video and MPEG free viewpoint video sequences as input, experimental results show that rate-constrained estimated 3D surfaces computed by our algorithm can reduce coding rate of depth maps by up to 32% compared with unconstrained estimated surfaces for the same quality of synthesized virtual views at the decoder.

The effect of optical blur on central and peripheral word visual acuity.

PURPOSE: We investigated how dioptric blur affected word acuity thresholds for targets presented at different retinal eccentricities. METHODS: Word thresholds were measured at 0, 5, and 10 degrees and for different Weber contrast levels of 4, 10, 45, and 90%. RESULTS: We find that increasing optical blur increased word acuity thresholds, but the extent of change was dependent on retinal eccentricity and stimulus contrast. In particular, the resolution reduction per diopter of blur (as indicated by the slope of lines fitted to data) was significantly less at peripheral locations (0 degrees vs. 5 and 10 degrees) and for low-contrast targets. CONCLUSIONS: These findings provide useful guidelines to predict how patients with contrast loss and/or those that rely upon an eccentric retinal location for reading respond to the introduction of optical blur in a clinical setting.