Related papers: Efficient Regularization of Squared Curvature

Integral field spectroscopy of high-redshift galaxies has become a powerful tool for understanding their dynamics and evolutionary states. However, in the case of gravitationally lensed systems, it has proved difficult to model both lensing…

Geometric rectification of images of distorted documents finds wide applications in document digitization and Optical Character Recognition (OCR). Although smoothly curved deformations have been widely investigated by many works, the most…

The presence of inhomogeneous media between optical sensors and objects leads to distorted imaging outputs, significantly complicating downstream image-processing tasks. A key challenge in image restoration is the lack of high-quality,…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

Uncertainty quantification for inverse problems in imaging has drawn much attention lately. Existing approaches towards this task define uncertainty regions based on probable values per pixel, while ignoring spatial correlations within the…

Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points. Each iteration of these methods involves computation of gradient,…

Product Quantization (PQ) has long been a mainstream for generating an exponentially large codebook at very low memory/time cost. Despite its success, PQ is still tricky for the decomposition of high-dimensional vector space, and the…

We study the problem of reconstructing an image from information stored at contour locations. We show that high-quality reconstructions with high fidelity to the source image can be obtained from sparse input, e.g., comprising less than…

Transformer architectures are now central to sequence modeling tasks. At its heart is the attention mechanism, which enables effective modeling of long-term dependencies in a sequence. Recently, transformers have been successfully applied…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…

In this paper we present methods for triangulation of infinite cylinders from image line silhouettes. We show numerically that linear estimation of a general quadric surface is inherently a badly posed problem. Instead we propose to…

Inverse problems defined naturally on the sphere are becoming increasingly of interest. In this article we provide a general framework for evaluation of inverse problems on the sphere, with a strong emphasis on flexibility and scalability.…

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…

Image resolution that has close relations with accuracy and computational cost plays a pivotal role in network training. In this paper, we observe that the reduced image retains relatively complete shape semantics but loses extensive…

In 3D shape reconstruction based on template mesh deformation, a regularization, such as smoothness energy, is employed to guide the reconstruction into a desirable direction. In this paper, we highlight an often overlooked property in the…

In inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with…

Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…

There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically…