New understanding of color perception theory

Image Sensors World        Go to the original article...

From phys.org a news article about a recent paper that casts doubt on the traditional understanding of how human color perception works: "Math error: A new study overturns 100-year-old understanding of color perception":

A new study corrects an important error in the 3D mathematical space developed by the Nobel Prize-winning physicist Erwin Schrödinger and others, and used by scientists and industry for more than 100 years to describe how your eye distinguishes one color from another. The research has the potential to boost scientific data visualizations, improve TVs and recalibrate the textile and paint industries.

The full paper appears in the Proceedings of the National Academy of Sciences vol. 119 no. 18 (2022). It is titled "The non-Riemannian nature of perceptual color space" authored by Dr. Roxana Bujack and colleagues at Los Alamos National Lab.

The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrödinger, that perceived color space is not Euclidean but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry. This finding is inconsistent with the current approaches to modeling perceptual color space. Therefore, the assumed shape of color space requires a paradigm shift. Consequences of this apply to color metrics that are currently used in image and video processing, color mapping, and the paint and textile industries. These metrics are valid only for small differences. Rethinking them outside of a Riemannian setting could provide a path to extending them to large differences. This finding further hints at the existence of a second-order Weber–Fechner law describing perceived differences.

 


The key observation that this paper rests on is the concept of "diminishing returns". Statistical analysis of experimental data collected in this paper suggests that the perceived difference between pairs of colors A, B and C that lie along a single shortest path (geodesic) do not satisfy the additive equality.

A commentary by Dr. David Brainard (U. Penn.) about this paper was published in PNAS and is available here: https://color2.psych.upenn.edu/brainard/papers/2022-BrainardPNASCommentary.pdf

Some of the caveats noted in this commentary piece:

First, the authors make a first principles assumption that the achromatic locus is a geodesic and use this in their choice of stimuli. This assumption is intuitively appealing in that it would be surprising that the shortest path in color space between two achromatic stimuli would involve a detour through a chromatic stimulus and back. However, the achromatic locus as a geodesic was not empirically established, and more work could be considered to shore up this aspect of the argument. Second, the data were collected using online methods and combined across subjects prior to the analysis. This raises the question of whether the aggregate performance analyzed could be non-Riemannian even when the performance of each individual subject was itself Riemannian. Although it is not immediately obvious whether this could occur, it might be further considered as a possibility.

Phys.org press release: https://phys.org/news/2022-08-math-error-overturns-year-old-perception.html

LANL press release: https://discover.lanl.gov/news/0810-color-perception

PNAS paper: https://www.pnas.org/doi/10.1073/pnas.2119753119

Go to the original article...

A Curious Observation about 1-bit Quanta Image Sensors Explained

Image Sensors World        Go to the original article...

Dr. Stanley Chan (Purdue University) has a preprint out titled "On the Insensitivity of Bit Density to Read Noise in One-bit Quanta Image Sensors" on arXiv. This paper presents a rigorous theoretical analysis of an intuitive but curious observation that was first made in the paper by E. Fossum titled "Analog read noise and quantizer threshold estimation from Quanta Image Sensor Bit Density."

Why is the quanta image sensor bit density insensitive to read noise at high enough exposure values?

The one-bit quanta image sensor is a photon-counting device that produces binary measurements where each bit represents the presence or absence of a photon. In the presence of read noise, the sensor quantizes the analog voltage into the binary bits using a threshold value q. The average number of ones in the bitstream is known as the bit-density and is often the sufficient statistics for signal estimation. An intriguing phenomenon is observed when the quanta exposure is at unity and the threshold is q=0.5. The bit-density demonstrates a complete insensitivity as long as the read noise level does not exceeds a certain limit. In other words, the bit density stays at a constant independent of the amount of read noise. This paper provides a mathematical explanation of the phenomenon by deriving conditions under which the phenomenon happens. It was found that the insensitivity holds when some forms of the symmetry of the underlying Poisson-Gaussian distribution holds.



The paper concludes:

The insensitivity of the bit density of a 1-bit quanta image sensor is analyzed. It was found that for a quanta exposure θ = 1 and an analog voltage threshold q = 0.5, the bit density D is nearly a constant whenever the read noise satisfies the condition σ ≤ 0.4419. The proof is derived by exploiting the symmetry of the Gaussian cumulative distribution function, and the symmetry of the Poisson probability mass function at the threshold k = 0.5. An approximation scheme is introduced to provide a simplified estimate where σ ≤ 1/√2π = 0.4. In general, the analysis shows that the insensitivity of the bit density is more of a (very) special case of the 1-bit quantized Poisson-Gaussian statistics. Insensitivity can be observed when the quanta exposure θ is an integer and the threshold is q = θ−0.5. As soon as the pair (θ, q) deviates from this configuration, the insensitivity will no longer appear.

Complete article can be downloaded here: https://arxiv.org/pdf/2203.06086

An early-access version of Eric's paper is available here: https://ieeexplore.ieee.org/document/9729893

Go to the original article...

css.php