Aximorphic Perspective Projection Model for Immersive Imagery

TL;DR

An extended perspective imaging model, which can represent distortion and FoV parameters of entire variety of film and photographic lenses, while preserving parametrization in an artistically convincing manner is presented.

Abstract

A wide choice of cinematic lenses enables motion-picture creators to adapt image visual-appearance to their creative vision. Such choice does not exist in the realm of real-time computer graphics, where only one type of perspective projection is widely used, a linear perspective. This paper presents an extended perspective imaging model, which can represent distortion and FoV parameters of entire variety of film and photographic lenses (e.g., wide-angle, fisheye, anamorphic), while preserving parametrization in an artistically convincing manner. Self-experimentation with the model revealed that each projection type provides accurate perception of a different aspect of depicted space (e.g., speed, distance, shape). Presented model, enables combination of multiple projections, each on a different axis of the image, to achieve optimal perception for a given scenario. This new projection, named aximorphic, was made available here, under an open license (CC BY-SA 3.0), for a wide and easy adoption.

Figures (6)

• Figure 1: Illustrating correlation between the aximorphic interpolation weights $\vec{\varphi}_x$, $\vec{\varphi}_y$ and the spherical angle $\varphi$.
• Figure 2: Plotting of vignetting intensity across the image radius, for each azimuthal projection at various $\Omega$ angles.
• Figure 3: Example of various wide--angle ($\Omega_v\approx110\text{\textdegree}$) aximorphic-azimuthal projections with vignetting in $4/3^2$ aspect-ratio. The checkerboard depicts a cube centered at the observation point, with each face colored according to the axis direction. Here, primary colors represent the positive axis, and neighboring complementary colors its negative equivalent (same as in the color-wheel), $\{Mg,Yl,Cy\}\mapsfrom-\ \{X,Y,Z\}\ +\mapsto\{R,G,B\}$.
• Figure 4: Mapping of $t\in[0,1]$ to spectral color $\vec{\chi}\in[0,1]^3$, for emulation of chromatic aberration. This is an output of periodic function, found in equation \ref{['eq:spectrum']}. Distribution of the values ensures proper color order and sum-of-samples with guarantied neutral-white tint.
• Figure 5: Example of aximorphic lens distortion with chromatic aberration, where $\vec{k}_{x1}=-0.25$, $\vec{k}_{y1}=0.04$, $d=0.5$, with 64--spectral samples.

Theorems & Definitions (1)

• Remark