Related papers: A Color Elastica Model for Vector-Valued Image Reg…
One classical approach to regularize color is to tream them as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the…
Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…
Euler's elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…
We propose a novel model for decomposing grayscale images into three distinct components: the structural part, representing sharp boundaries and regions with strong light-to-dark transitions; the smooth part, capturing soft shadows and…
Image segmentation is a fundamental topic in image processing and has been studied for many decades. Deep learning-based supervised segmentation models have achieved state-of-the-art performance but most of them are limited by using…
Euler's Elastica based unsupervised segmentation models have strong capability of completing the missing boundaries for existing objects in a clean image, but they are not working well for noisy images. This paper aims to establish a…
The Euler Elastica (EE) model with surface curvature can generate artifact-free results compared with the traditional total variation regularization model in image processing. However, strong nonlinearity and singularity due to the…
This paper concerns an optimization algorithm for unconstrained non-convex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving numerical integrator,…
In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in…
Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…
Image vectorization is a process to convert a raster image into a scalable vector graphic format. Objective is to effectively remove the pixelization effect while representing boundaries of image by scaleable parameterized curves. We…
The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which…
We consider curvature depending variational models for image regularization, such as Euler's elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape-and image…
In this paper, we propose a novel curvature-penalized minimal path model via an orientation-lifted Finsler metric and the Euler elastica curve. The original minimal path model computes the globally minimal geodesic by solving an Eikonal…
After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing…
The task of image segmentation is to classify each pixel in the image based on the appropriate label. Various deep learning approaches have been proposed for image segmentation that offers high accuracy and deep architecture. However, the…