Elliptification of Rectangular Imagery

We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We will focus primarily on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with invertible mappings between the square and the circular disc then extend it to handle rectangles and ellipses. This extension can be done by simply removing the eccentricity and reintroducing it back after using a chosen square-to-disc mapping.

Revolvable Indoor Panoramas Using a Rectified Azimuthal Projection

We present an algorithm for converting an indoor spherical panorama into a photograph with a simulated overhead view. The resulting image will have an extremely wide field of view covering up to 4{\pi} steradians of the spherical panorama. We argue that our method complements the stereographic projection commonly used in the "little planet" effect. The stereographic projection works well in creating little planets of outdoor scenes; whereas our method is a well-suited counterpart for indoor scenes. The main innovation of our method is the introduction of a novel azimuthal map projection that can smoothly blend between the stereographic projection and the Lambert azimuthal equal-area projection. Our projection has an adjustable parameter that allows one to control and compromise between distortions in shape and distortions in size within the projected panorama. This extra control parameter gives our projection the ability to produce superior results over the stereographic projection.

Warping Peirce Quincuncial Panoramas

The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic applications. In this paper, we propose an algorithm and user-interface to mitigate these artifacts. Moreover, in order to facilitate an interactive user-interface, we present a fast algorithm for calculating the Peirce quincuncial projection of spherical imagery. We then promote the Peirce quincuncial projection as a viable alternative to the more popular stereographic projection in some scenarios.