We propose an approximated L_1 curvature model to reconstruct implicit surfaces from unstructured point cloud data. The L_1 curvature |κ | keeps sharp features better than a typical κ ^2 based curvature models, yet it is computationally more challenging. We approximate the L_1 curvature by a smooth function, consider the reconstructed implicit surfaces as a denoised signed distance function (SDF), and propose a simple gradient descent scheme for fast and efficient computation. We demonstrate not only the effectiveness of the model but also the advantages of considering the L_1 curvature.
Multi-object segmentation algorithms are of great interest in a very large range of fields. Deep learning brought major improvements in terms of processing speed or prediction accuracy. Nevertheless, some traditional methods such as active surfaces have features that conventional deep learning methods cannot provide, especially representing the object in a continuous geometrical way and encoding prior information on the shapes to segment. Those features are of particular interest in biology to efficiently segment noisy and poorly resolved data, and then understand the interactions between segmented cells. We introduce NAGINI-3D (N-Active shapes for seGmentINg 3D biological Images), a new hybrid segmentation method dedicated to multi-object segmentation of 3D images that combines the efficiency of deep learning and the powerful representation of active surfaces. We evaluate our method on real and synthetic 3D datasets of fluorescence microscopy.
Using classical smoothers in restoration processes, such as total variation regularisation, while capturing well discontinuities, is known to induce an estimation bias in the final result, materialised by a loss of contrast. If the literature is prolific when dealing with standard modalities of images (grayscale or RGB images), it is more tenuous when the involved modality encodes some intrinsic geometrical properties, requiring the design of specific purpose-built algorithms. In this work, focused on such a specific modality, namely polarimetric imaging, we address the joint restoration and contrast re-enhancement (equivalently referred to as debiasing or refitting) question within an extension of the CLEAR framework (Covariant LEAst-square Refitting, [5]), emphasising the importance of preserving the Jacobian (with respect to the observed signal) of the original estimator.
We propose a functional for extracting curves between a list of possible endpoints, based on a discretization of a variational energy and Smirnov's decomposition theorem for vector fields. It is then used to design a bi-level minimization approach to automatically extract curves and 1D structures from an image, which is mostly unsupervised.
We present a proof-of-concept study demonstrating the application of the linear osmotic flow to unstructured domains in ℝ^3 , such as irregular meshes. This study aims to extend the osmotic filter to surfaces, thereby simplifying some geometry processing tasks, such as surface inpainting and completion (cloning), that typically require costly and complex algorithms. This will include two new challenges: the numerical solution of the drift-diffusion osmotic model on meshes, and the use of surface geometric descriptors, which play the role of reference function for the osmotic flow.
