Lijun Ding

Bio: Lijun Ding is an academic researcher from Wright State University. The author has contributed to research in topics: Mathematics & Computer science. The author has an hindex of 2, co-authored 2 publications receiving 460 citations.

Volumetric image registration by template matching

Abstract: A template-matching approach to registration of volumetric images is described. The process automatically selects about a dozen highly detailed and unique templates (cubic or spherical subvolumes) from the target volume and locates the templates in the reference volume. The centroids of the 'best' four correspondences are then used to determine the transformation matrix that resamples the target volume to overlay the reference volume. Different similarity measures used in template matching are discussed and preliminary results are presented. The proposed registration method produces a median error of 2.8 mm when registering Venderbilt image data sets, with average registration time of 2.5 minutes on a 400 MHz PC.

Algorithmic Regularization in Model-free Overparametrized Asymmetric Matrix Factorization

Abstract: We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed matrix, where the global optima provably overfit. We show that vanilla gradient descent with small random initialization sequentially recovers the principal components of the observed matrix. Consequently, when equipped with proper early stopping, gradient descent produces the best low-rank approximation of the observed matrix without explicit regularization. We provide a sharp characterization of the relationship between the approximation error, iteration complexity, initialization size and stepsize. Our complexity bound is almost dimension-free and depends logarithmically on the approximation error, with significantly more lenient requirements on the stepsize and initialization compared to prior work. Our theoretical results provide accurate prediction for the behavior gradient descent, showing good agreement with numerical experiments.

Flat minima generalize for low-rank matrix recovery

Abstract: Empirical evidence suggests that for a variety of overparameterized nonlinear models, most notably in neural network training, the growth of the loss around a minimizer strongly impacts its performance. Flat minima -- those around which the loss grows slowly -- appear to generalize well. This work takes a step towards understanding this phenomenon by focusing on the simplest class of overparameterized nonlinear models: those arising in low-rank matrix recovery. We analyze overparameterized matrix and bilinear sensing, robust PCA, covariance matrix estimation, and single hidden layer neural networks with quadratic activation functions. In all cases, we show that flat minima, measured by the trace of the Hessian, exactly recover the ground truth under standard statistical assumptions. For matrix completion, we establish weak recovery, although empirical evidence suggests exact recovery holds here as well. We conclude with synthetic experiments that illustrate our findings and discuss the effect of depth on flat solutions.

A Validation Approach to Over-parameterized Matrix and Image Recovery

Abstract: In this paper, we study the problem of recovering a low-rank matrix from a number of noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a prior and use an overspecified factored representation of the matrix variable, where the global optimal solutions overfit and do not correspond to the underlying ground-truth. We then solve the associated nonconvex problem using gradient descent with small random initialization. We show that as long as the measurement operators satisfy the restricted isometry property (RIP) with its rank parameter scaling with the rank of ground-truth matrix rather than scaling with the overspecified matrix variable, gradient descent iterations are on a particular trajectory towards the ground-truth matrix and achieve nearly information-theoretically optimal recovery when stop appropriately. We then propose an efficient early stopping strategy based on the common hold-out method and show that it detects nearly optimal estimator provably. Moreover, experiments show that the proposed validation approach can also be efficiently used for image restoration with deep image prior which over-parameterizes an image with a deep network.

Assessment of Very High Spatial Resolution Satellite Image Segmentations

Abstract: Since 1999, very high spatial resolution satellite data represent the surface of the Earth with more detail. However, information extraction by per pixel multispectral classification techniques proves to be very complex owing to the internal variability increase in land-cover units and to the weakness of spectral resolution. Image segmentation before classification was proposed as an alternative approach, but a large variety of segmentation algorithms were developed during the last 20 years, and a comparison of their implementation on very high spatial resolution images is necessary. In this study, four algorithms from the two main groups of segmentation algorithms (boundarybased and region-based) were evaluated and compared. In order to compare the algorithms, an evaluation of each algorithm was carried out with empirical discrepancy evaluation methods. This evaluation is carried out with a visual segmentation of Ikonos panchromatic images. The results show that the choice of parameters is very important and has a great influence on the segmentation results. The selected boundary-based algorithms are sensitive to the noise or texture. Better results are obtained with regionbased algorithms, but a problem with the transition zones between the contrasted objects can be present.

Depth-based human fall detection via shape features and improved extreme learning machine

Abstract: Falls are one of the major causes leading to injury of elderly people. Using wearable devices for fall detection has a high cost and may cause inconvenience to the daily lives of the elderly. In this paper, we present an automated fall detection approach that requires only a low-cost depth camera. Our approach combines two computer vision techniques-shape-based fall characterization and a learning-based classifier to distinguish falls from other daily actions. Given a fall video clip, we extract curvature scale space (CSS) features of human silhouettes at each frame and represent the action by a bag of CSS words (BoCSS). Then, we utilize the extreme learning machine (ELM) classifier to identify the BoCSS representation of a fall from those of other actions. In order to eliminate the sensitivity of ELM to its hyperparameters, we present a variable-length particle swarm optimization algorithm to optimize the number of hidden neurons, corresponding input weights, and biases of ELM. Using a low-cost Kinect depth camera, we build an action dataset that consists of six types of actions (falling, bending, sitting, squatting, walking, and lying) from ten subjects. Experimenting with the dataset shows that our approach can achieve up to 91.15% sensitivity, 77.14% specificity, and 86.83% accuracy. On a public dataset, our approach performs comparably to state-of-the-art fall detection methods that need multiple cameras.

Evaluating Pavement Cracks with Bidimensional Empirical Mode Decomposition

Abstract: Crack evaluation is essential for effective classification of pavement cracks. Digital images of pavement cracks have been analyzed using techniques such as fuzzy set theory and neural networks. Bidimensional empirical mode decomposition (BEMD), a new image analysis method recently developed, can potentially be used for pavement crack evaluation. BEMD is an extension of the empirical mode decomposition (EMD), which can decompose nonlinear and nonstationary signals into basis functions called intrinsic mode functions (IMFs). IMFs are monocomponent functions that have well-defined instantaneous frequencies. EMD is a sifting process that is nonparametric and data driven; it does not depend on an a priori basis set. It is able to remove noise from signals without complicated convolution processes. BEMD decomposes an image into two-dimensional IMFs. The present paper explores pavement crack detection using BEMD together with the Sobel edge detector. A number of images are filtered with BEMD to remove noise, and the residual image analyzed with the Sobel edge detector for crack detection. The results are compared with results from the Canny edge detector, which uses a Gaussian filter for image smoothing before performing edge detection. The objective is to qualitatively explore how well BEMD is able to smooth an image for more effective edge detection with the Sobel method.