Projection is the process of forming a 2D image from a 3D scene. Perspective projection is formed by rays reflected from the objects through the optical center (or focal center) onto a capturing device (CCD or film). To avoid reversal of the image we usually assume that the capturing device lies in front of the optical center. We form a coordinate system by setting the origin O = (0, 0, 0) at t...

This project is to investigate the problem of choosing point locations on the surface of a unit sphere in R such that the projection of the points onto any plane in R is visually dissimilar to the projection onto all other planes in R. The optimal set of point locations is the set that minimizes the similarity among all projections. The problem is a nonlinear inequality problem with quadratic c...

Point-of-gaze estimation systems estimate the point within the visual field that is imaged on the highest acuity region of the retina known as the fovea. A new method has been introduced that estimates point-of-gaze by exploiting the invariance property of cross-ratios in projective transformations [1]. The projective transformation is formed by two perspective projections. The first projection...

One of the most interesting tasks of scene analysis is the reconstruction problem, which is the problem of finding a three-dimensional description of a scene from two or more projections. When the scene is assumed to be composed of man-made objects bounded by quadric surfaces, the reconstruction process is simplified if the border lines in each projection are given by means of straight-line seg...

Given two rational, properly parametrized space curves C1 and C2, where C2 is contained in some plane Π, we provide an algorithm to check whether or not there exist perspective or parallel projections mapping C1 onto C2, i.e. to recognize C2 as the projection of C1. In the affirmative case, the algorithm provides the eye point(s) of the perspective transformation(s), or the direction(s) of the ...

Images are formed as projections of the three-dimensional world onto a two-dimensional light-sensing surface. The brightness of the image at each point indicates how much light was absorbed by the surface at that spatial position at a particular time (or over some interval of time). When an object in the world moves relative to the sensor surface, the two-dimensional projection of that object m...

BACKGROUND Breast projection is a critical element of breast reconstruction aesthetics, but little has been published regarding breast projection as the firm expander is changed to a softer implant. Quantitative data representing this loss in projection may enhance patient education and improve our management of patient expectations. METHODS Female patients who were undergoing immediate tissu...

Loop closure detection (LCD) can effectively eliminate the cumulative errors in simultaneous localization and mapping (SLAM) by detecting position of a revisit building interframe pose constraint relations. However, real-world natural scenes, driverless ground vehicles or robots usually same place from different position, meaning that descriptor cannot give uniform description similar failing L...

Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of point-sampled models and increasingly adopted as the standard definition of point set surfaces. We classify the ...