A Study on Spectral Response for Dichromatic Vision

The paper proposes a novel approach to analyze the dichromatic color vision defects from a point of spectral responses based on the projection theory of spectral space to/from 2-D dichromatic Human Visual Sub-Space. The visible spectra to the dichromats (protanopes, deutanopes, and tritanopes) are extracted from an n-dimensional spectral input with the 2-D version of Matrix-R notated as Rdichro. Since the matrix Rdichro is an identical and invariant mapping operator inherent in human vision that is independent of any linear transformation or any illuminant, the fundamental spectra C*dichro sensed with matrix Rdichro are also inherent in the dichromats. The lost spectra are easily obtained as a difference in the fundamentals between the normals and the the dichromats. These lost spectral profiles tell us why the color appearances are similar to the protanopes and deutanopes, and dissimilar to the tritanopes.The perceived colors are simulated based on the two hypotheses of substitution and nulling processes. Introduction Color vision deficiency is quite common, about 8% males have any of color blindness. So far, many approaches to simulate the color deficiencies have been reported. Dichromatic color vision arises from missing one of the LMS cones, L type in protanopes, M type in deuteranopes, and S type in tritanopes. In comparison with normal trichromatic vision, dichromats mistake a color discrimination in the reduced 2-D color gamut. Brettel et al [1] proposed a solution to this problem and Viénot et al [2] advanced the model to a palette-based graphical simulation system on sRGB display. Since different colors (Gamut I) can be perceived by a dichromat as equal to the test stimulus T, the simulation S is to get the intersection of Gamut I and to find the set of colored stimuli (Gamut II) whose appearance is the same for normals as for dichromat. However their algorithm has the drawbacks in the high computation costs and especially in the difficulty of determining the Gamut II. Recently, P.Capilla et al [3], simplified the corresponding pair procedure through the Gamut I and Gamut II into a systematic color transform model of T to/from S based on the following two hypothetheses as [A] Substitution hypothesis: Dichromacy arises from the substitution of one photopigment by another (M by L for protanopes, L by M for deuteranopes, and L or M by S for tritanopes), but the subsequent neural circuitry is normal. [B] Nulling hypothesis: One of the opponent chromatic mechanisms (red-green for protanopes and deuteranopes, blue-yellow for tritanopes) is nulled in some or all of the opponent stages of the model. These models simulate a dichromatic vision on display screen just as a normal observer experiences the same sensation viewing S as a dichromat viewing T through RGB to LMS and further into the opponent-color space such as ATD and through their inverse transformations. However, since these models are described by tri-color signals, we can know the lost colors in dichromatic vision only as the color differences in tri-color space, not in the spectral space. This paper discusses the dichromatic color vision based on the spectral responses and clarifies what parts in the spectra visible to the nomals are lost for the dichromats of protanopes, deuteranopes and tritanopes. A dichromatic view on display is also simulated according to the method by P.Capilla not using ATD (Guth) but with IPT [4] (Ebner & Fairchild) as an opponent color space. A simulated image is compared with those by existing algorithms. Basic Concept The paper introduces a novel approach to the dichromatic vision from a point of spectral analysis as follows. [1] Projection to Dichromatic Fundamentals Based on the projection theory, a n-dimensional spectral input is projected onto 2-dimensional dichromatic HVSS (Human Visual Sub-Space), that is, the dichromatic FCS (Fundamental Color Space). In the dichromatic FCS, the fundamentals, are extracted as the spectral components visible to the dichromats based on the 2-D version of matrix-R theory. [2] Extraction of Lost Spectra for Dichromats The spectral responses are analyzed using sinusoidal SPDs (Spectral Power Distributions) and typical spectral color targets such as Macbeth, IT8 or Munsell. The lost spectra are simply extracted as the differences in the fundamentals captured by the nomals and the dichromats through the projection matrix Rdichro. [3] Color Appearance Simulation The substitution and the nulling hypotheses on the dichromats are applied to the LMS cone space and the IPT opponent-color space respectively. The simulated colors for dichromats are calculated by inserting the substitution and the nulling processes in between the forward and backward transformation path ways. IPT is adopted because it’s an excellent opponent-color space with hue linearlities and choromatic uniformities [5]. Figure 1 overviews the proposed model. The key to the new approach lies in the introduction of modified dichromatic version of matrix-R, here notated as Rdichro. The model is roughly divided into two stages. In the first half stage, the fundamentals, spectra visible to dichromats are extracted through Rdichro.and the lost spectra are easily analyzed by comparing with fundamentals for normals. The latter half stage simulates the colors to be viewed on display for normals just as experiencing the similar color appearance as the dichromats, where the fundamental spectra perceived by dichromats are converted to the corresponding LMS /sRGB signals through the inverse processes. In the path of latter stage, the conversion from LMS to IPT is included to reflect an opponent-color encoding function in human brain. The inverse signal processings in the latter stage are generally the same as Capilla, originating from Brettel and Viénot. 8 ©2011 Society for Imaging Science and Technology Figure 1 Overview of proposed model (in case of dichromatic vision for protanopes) Projection to Dichromatic Fundamentals A color matching function (cmf) A transforms a ndimensional spectral input C into the tri-stimulus vector T =XYZ. While, according to “matrix R” theory [6], C is decomposed into the fundamental C* and metameric black B in the HVSS as [ ] transpose t , C C C t n = = ) ( ) ( ) ( 2 1 λ λ λ L C (1) C R I B RC C B C C ) ( , − = = + = , * * (2) I denotes unit matrix and the projector R onto HVSS is derived from CMF A as t t A A A A R -1 ) ( = (3) A is the n × 3 matrix of 1931CIE ) ( ) ( ) ( λ z , λ y , λ x cmf. The fundamental C* is the essential spectrum to the normal trichromatic vision that carries the the intrinsic color stimulus, perceived as the unique XYZ tri-stimulus sensation. The metameric black B is the residue insensitive to human vision and spans n-3 dimensional null space. Here, the projection matrix RLMS from n-dimensional spectral space to 3-dimensional LMS space is derived by replacing the cmf A with cmf ALMS as follows. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )