Related papers: Tropical Geometry Based Edge Detection Using Min-P…
Let $K$ be a field equipped with a valuation. Tropical varieties over $K$ can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of $K$.Because of the use of the valuation, the theory of tropical Gr{\"o}bner…
In this note, we propose a novel technique to reduce the algorithmic complexity of neural network training by using matrices of tropical real numbers instead of matrices of real numbers. Since the tropical arithmetics replaces…
Many biochemical measurements define state spaces that are bounded, absorbing, and physically irreversible, yet are routinely analysed using linear and Euclidean frameworks that assume global invertibility, symmetry, and translation…
Temporal action detection (TAD) aims to identify and localize action instances in untrimmed videos, which is essential for various video understanding tasks. However, recent improvements in model performance, driven by larger feature…
In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an…
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against state-of-the-art attacks, including the Carlini-Wagner…
Mask-guided matting networks have achieved significant improvements and have shown great potential in practical applications in recent years. However, simply learning matting representation from synthetic and lack-of-real-world-diversity…
In this paper, we aim to develop an efficient and compact deep network for RGB-D salient object detection, where the depth image provides complementary information to boost performance in complex scenarios. Starting from a coarse initial…
Based on a nonlocal Laplacian operator, a novel edge detection method of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge…
Benefiting from the spatial cues embedded in depth images, recent progress on RGB-D saliency detection shows impressive ability on some challenge scenarios. However, there are still two limitations. One hand is that the pooling and…
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute the positive tropicalization, offering a real analogue to…
We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…
In this paper, we propose a novel edge preserving and multi-scale contextual neural network for salient object detection. The proposed framework is aiming to address two limits of the existing CNN based methods. First, region-based CNN…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…
In this work the method of masks, creating and using of inverted image masks, together with binary operation of image data are used in edge detection of binary images, monochrome images, which yields about 300 times faster than ordinary…
We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional space,…
Accurate detection of the centerline of a thick linear structure and good estimation of its thickness are challenging topics in many real-world applications such X-ray imaging, remote sensing and lane marking detection in road traffic.…
Gabor wavelet is an essential tool for image analysis and computer vision tasks. Local structure tensors with multiple scales are widely used in local feature extraction. Our research indicates that the current corner detection method based…
Edge detection has made significant progress with the help of deep Convolutional Networks (ConvNet). These ConvNet based edge detectors have approached human level performance on standard benchmarks. We provide a systematical study of these…