Related papers: Euler Characteristic Transform Based Topological L…

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with…

While many works focus on 3D reconstruction from images, in this paper, we focus on 3D shape reconstruction and completion from a variety of 3D inputs, which are deficient in some respect: low and high resolution voxels, sparse and dense…

Monocular 3D face reconstruction plays a crucial role in avatar generation, with significant demand in web-related applications such as generating virtual financial advisors in FinTech. Current reconstruction methods predominantly rely on…

Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior…

Deep learning affords enormous opportunities to augment the armamentarium of biomedical imaging, albeit its design and implementation have potential flaws. Fundamentally, most deep learning models are driven entirely by data without…

In the last years, deep learning has dramatically improved the performances in a variety of medical image analysis applications. Among different types of deep learning models, convolutional neural networks have been among the most…

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Topological integral transforms have found many applications in shape analysis, from prediction of clinical outcomes in brain cancer to analysis of barley seeds. Using Euler characteristic as a measure, these objects record rich geometric…

In this paper, we revisit the long-standing problem of automatic reconstruction of 3D objects from single line drawings. Previous optimization-based methods can generate compact and accurate 3D models, but their success rates depend heavily…

Current methods for 3D object reconstruction from a set of planar cross-sections still struggle to capture detailed topology or require a considerable number of cross-sections. In this paper, we present, to the best of our knowledge the…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…

The Euler Characteristic Transform (ECT) is a robust method for shape classification. It takes an embedded shape and, for each direction, computes a piecewise constant function representing the Euler Characteristic of the shape's sublevel…

Capturing the global topology of an image is essential for proposing an accurate segmentation of its domain. However, most of existing segmentation methods do not preserve the initial topology of the given input, which is detrimental for…

Automatic 3D neuron reconstruction is critical for analysing the morphology and functionality of neurons in brain circuit activities. However, the performance of existing tracing algorithms is hinged by the low image quality. Recently, a…

The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the Local Euler Characteristic Transform ($\ell$-ECT), a novel…

Sharp features such as edges and corners play an important role in the perception of 3D models. In order to capture them better, we propose quadric loss, a point-surface loss function, which minimizes the quadric error between the…

Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…