相关论文: Warping Peirce Quincuncial Panoramas

We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that…

In this paper, we study alternating projections on nontangential manifolds based on the tangent spaces. The main motivation is that the projection of a point onto a manifold can be computational expensive. We propose to use the tangent…

Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…

In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B\'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…

Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…

Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant…

Controllable spherical panoramic image generation holds substantial applicative potential across a variety of domains.However, it remains a challenging task due to the inherent spherical distortion and geometry characteristics, resulting in…

Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…

The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on…

Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved…

Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…

Image stitching algorithms often adopt the global transformation, such as homography, and work well for planar scenes or parallax free camera motions. However, these conditions are easily violated in practice. With casual camera motions,…

Spherometer is an instrument widely used for measuring the radius of curvature of a spherical surface. Cylindrometer is a modified spherometer, which can measure the radii of both spherical and cylindrical surfaces. Both of these…

Ptychography is a technique widely used in microscopy for achieving high-resolution imaging. This method relies on computational processing of images gathered from diffraction patterns produced by several partial illuminations of a sample.…

A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…

The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to…

Many imaging technologies rely on tomographic reconstruction, which requires solving a multidimensional inverse problem given a finite number of projections. Backprojection is a popular class of algorithm for tomographic reconstruction,…

The paper introduces cycles cross ratio, which extends the classic cross ratio of four points to various settings: conformal geometry, Lie spheres geometry, etc. Just like its classic counterpart cycles cross ratio is a measure of…

We present a novel solution to the camera pose estimation problem, where rotation and translation of a camera between two views are estimated from matched feature points in the images. The camera pose estimation problem is traditionally…