SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.Comment: Presented at CVPR 201

Arcfinder: An algorithm for the automatic detection of gravitational arcs

We present an efficient algorithm designed for and capable of detecting elongated, thin features such as lines and curves in astronomical images, and its application to the automatic detection of gravitational arcs. The algorithm is sufficiently robust to detect such features even if their surface brightness is near the pixel noise in the image, yet the amount of spurious detections is low. The algorithm subdivides the image into a grid of overlapping cells which are iteratively shifted towards a local centre of brightness in their immediate neighbourhood. It then computes the ellipticity for each cell, and combines cells with correlated ellipticities into objects. These are combined to graphs in a next step, which are then further processed to determine properties of the detected objects. We demonstrate the operation and the efficiency of the algorithm applying it to HST images of galaxy clusters known to contain gravitational arcs. The algorithm completes the analysis of an image with 3000x3000 pixels in about 4 seconds on an ordinary desktop PC. We discuss further applications, the method's remaining problems and possible approaches to their solution.Comment: 12 pages, 12 figure