Weak Visibility Queries of Line Segments in Simple Polygons

Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and O(n) space that can compute the visibility polygon for any query line segment s in O(k log n) time, where k is the size of the visibility polygon of s and n is the number of vertices of P. Alternatively, we build a data structure in O(n^3) time and O(n^3) space that can compute the visibility polygon for any query line segment in O(k + log n) time.Comment: 16 pages, 9 figures. A preliminary version of this paper appeared in ISAAC 2012 and we have improved results in this full versio

Optimizing Memory Efficiency for Convolution Kernels on Kepler GPUs

Convolution is a fundamental operation in many applications, such as computer vision, natural language processing, image processing, etc. Recent successes of convolutional neural networks in various deep learning applications put even higher demand on fast convolution. The high computation throughput and memory bandwidth of graphics processing units (GPUs) make GPUs a natural choice for accelerating convolution operations. However, maximally exploiting the available memory bandwidth of GPUs for convolution is a challenging task. This paper introduces a general model to address the mismatch between the memory bank width of GPUs and computation data width of threads. Based on this model, we develop two convolution kernels, one for the general case and the other for a special case with one input channel. By carefully optimizing memory access patterns and computation patterns, we design a communication-optimized kernel for the special case and a communication-reduced kernel for the general case. Experimental data based on implementations on Kepler GPUs show that our kernels achieve 5.16X and 35.5% average performance improvement over the latest cuDNN library, for the special case and the general case, respectively

Algorithms on Minimizing the Maximum Sensor Movement for Barrier Coverage of a Linear Domain

In this paper, we study the problem of moving $n$ sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether this problem on sensors with arbitrary sensing ranges is solvable in polynomial time. We settle this open question positively by giving an $O(n^2 \log n)$ time algorithm. For the special case when all sensors have the same-size sensing range, the previously best solution takes $O(n^2)$ time. We present an $O(n \log n)$ time algorithm for this case; further, if all sensors are initially located on the coverage segment, our algorithm takes $O(n)$ time. Also, we extend our techniques to the cycle version of the problem where the barrier coverage is for a simple cycle and the sensors are allowed to move only along the cycle. For sensors with the same-size sensing range, we solve the cycle version in $O(n)$ time, improving the previously best $O(n^2)$ time solution.Comment: This version corrected an error in the proof of Lemma 2 in the previous version and the version published in DCG 2013. Lemma 2 is for proving the correctness of an algorithm (see the footnote of Page 9 for why the previous proof is incorrect). Everything else of the paper does not change. All algorithms in the paper are exactly the same as before and their time complexities do not change eithe

Neuron Segmentation Using Deep Complete Bipartite Networks

In this paper, we consider the problem of automatically segmenting neuronal cells in dual-color confocal microscopy images. This problem is a key task in various quantitative analysis applications in neuroscience, such as tracing cell genesis in Danio rerio (zebrafish) brains. Deep learning, especially using fully convolutional networks (FCN), has profoundly changed segmentation research in biomedical imaging. We face two major challenges in this problem. First, neuronal cells may form dense clusters, making it difficult to correctly identify all individual cells (even to human experts). Consequently, segmentation results of the known FCN-type models are not accurate enough. Second, pixel-wise ground truth is difficult to obtain. Only a limited amount of approximate instance-wise annotation can be collected, which makes the training of FCN models quite cumbersome. We propose a new FCN-type deep learning model, called deep complete bipartite networks (CB-Net), and a new scheme for leveraging approximate instance-wise annotation to train our pixel-wise prediction model. Evaluated using seven real datasets, our proposed new CB-Net model outperforms the state-of-the-art FCN models and produces neuron segmentation results of remarkable qualityComment: miccai 201