Real-time High Resolution Fusion of Depth Maps on GPU

A system for live high quality surface reconstruction using a single moving depth camera on a commodity hardware is presented. High accuracy and real-time frame rate is achieved by utilizing graphics hardware computing capabilities via OpenCL and by using sparse data structure for volumetric surface representation. Depth sensor pose is estimated by combining serial texture registration algorithm with iterative closest points algorithm (ICP) aligning obtained depth map to the estimated scene model. Aligned surface is then fused into the scene. Kalman filter is used to improve fusion quality. Truncated signed distance function (TSDF) stored as block-based sparse buffer is used to represent surface. Use of sparse data structure greatly increases accuracy of scanned surfaces and maximum scanning area. Traditional GPU implementation of volumetric rendering and fusion algorithms were modified to exploit sparsity to achieve desired performance. Incorporation of texture registration for sensor pose estimation and Kalman filter for measurement integration improved accuracy and robustness of scanning process

Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data

Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observation regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability. We provide two strategies for this critical choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, and a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using simulation studies, and real applications to estimation of fractional anisotropy profiles based on diffusion tensor imaging measurements, growth velocity functions and bone mineral density curves.No embarg

Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Sparsity-Based Super Resolution for SEM Images

The scanning electron microscope (SEM) produces an image of a sample by scanning it with a focused beam of electrons. The electrons interact with the atoms in the sample, which emit secondary electrons that contain information about the surface topography and composition. The sample is scanned by the electron beam point by point, until an image of the surface is formed. Since its invention in 1942, SEMs have become paramount in the discovery and understanding of the nanometer world, and today it is extensively used for both research and in industry. In principle, SEMs can achieve resolution better than one nanometer. However, for many applications, working at sub-nanometer resolution implies an exceedingly large number of scanning points. For exactly this reason, the SEM diagnostics of microelectronic chips is performed either at high resolution (HR) over a small area or at low resolution (LR) while capturing a larger portion of the chip. Here, we employ sparse coding and dictionary learning to algorithmically enhance LR SEM images of microelectronic chips up to the level of the HR images acquired by slow SEM scans, while considerably reducing the noise. Our methodology consists of two steps: an offline stage of learning a joint dictionary from a sequence of LR and HR images of the same region in the chip, followed by a fast-online super-resolution step where the resolution of a new LR image is enhanced. We provide several examples with typical chips used in the microelectronics industry, as well as a statistical study on arbitrary images with characteristic structural features. Conceptually, our method works well when the images have similar characteristics. This work demonstrates that employing sparsity concepts can greatly improve the performance of SEM, thereby considerably increasing the scanning throughput without compromising on analysis quality and resolution.Comment: Final publication available at ACS Nano Letter

Application of Compressive Sensing Theory for the Reconstruction of Signals in Plastic Scintillators

Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals from measurements of plastic scintillators. Sparse representation of obtained signals was found using SVD transform.Comment: 7 pages, 3 figures; Presented at Symposium on applied nuclear physics and innovative technologies, Cracow, 03-06 June 201

Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

Efficient Registration of Pathological Images: A Joint PCA/Image-Reconstruction Approach

Registration involving one or more images containing pathologies is challenging, as standard image similarity measures and spatial transforms cannot account for common changes due to pathologies. Low-rank/Sparse (LRS) decomposition removes pathologies prior to registration; however, LRS is memory-demanding and slow, which limits its use on larger data sets. Additionally, LRS blurs normal tissue regions, which may degrade registration performance. This paper proposes an efficient alternative to LRS: (1) normal tissue appearance is captured by principal component analysis (PCA) and (2) blurring is avoided by an integrated model for pathology removal and image reconstruction. Results on synthetic and BRATS 2015 data demonstrate its utility.Comment: Accepted as a conference paper for ISBI 201