Design of a Trichromatic Cone Array

Cones with peak sensitivity to light at long (L), medium (M) and short (S) wavelengths are unequal in number on the human retina: S cones are rare (<10%) while increasing in fraction from center to periphery, and the L/M cone proportions are highly variable between individuals. What optical properties of the eye, and statistical properties of natural scenes, might drive this organization? We found that the spatial-chromatic structure of natural scenes was largely symmetric between the L, M and S sensitivity bands. Given this symmetry, short wavelength attenuation by ocular media gave L/M cones a modest signal-to-noise advantage, which was amplified, especially in the denser central retina, by long-wavelength accommodation of the lens. Meanwhile, total information represented by the cone mosaic remained relatively insensitive to L/M proportions. Thus, the observed cone array design along with a long-wavelength accommodated lens provides a selective advantage: it is maximally informative

Subspace Procrustes Analysis

Abstract. Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uni-form sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) for-mulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.

Finding a Colour Filter to Make a Camera Colorimetric by Optimisation

The Luther condition states that a camera is colorimetric if its spectral sensitivities are a linear transform from the XYZ colour matching functions. Recently, a method has been proposed for finding the optimal coloured filter that when placed in front of a camera, results in effective sensitivities that satisfy the Luther condition. The advantage of this method is that it finds the best filter for all possible physical capture conditions. The disadvantage is that the statistical information of typical scenes are not taken into account. In this paper we set forth a method for finding the optimal filter given a set of typical surfaces and lights. The problem is formulated as a bilinear least-squares estimation problem (linear both in the filter and the colour correction). This is solved using Alternating Least-Squares (ALS) technique. For a range of cameras we show that it is possible to find an optimal colour correction filter with respect to which the cameras are almost colorimetric

Spectral caustic rendering of a homogeneous caustic object based on wavelength clustering and eye sensitivity

In the real world, the index of refraction of a refractive object (caustic object) varies across the wavelengths. Therefore, in physically based caustic rendering, we need to take into account spectral information. However, this may lead to prohibitive running time. In response, we propose a two-step acceleration scheme for spectral caustic rendering. Our acceleration scheme takes into account information across visible wavelengths of the scene, that is, the index of refraction (IOR) (caustic object), light power (light), and material reflectance (surface). To process visible wavelengths effectively, firstly we cluster the wavelengths which have similar first refraction (air to caustic object) directions. In this way, all the wavelengths in a cluster can be represented by one light ray during rendering. Secondly, by considering the surrounding objects (their material reflectance from and visible surface area of the caustic objects) and light power, we compute the refinement amount of each wavelength cluster. Our accelerated algorithm can produce photorealistic rendering results close to their reference images (which are generated by rendering every 1 nm of visible wavelengths) with a significant acceleration magnitude. Computational experiment results and comparative analyses are reported in the paper.Accepted versio