Supplementary material

Supplementary Material September 2025 1 PBRT example The Physically Based Rendering Toolkit (PBRT) is a rendering system that implements the mathematical principles of modern photorealistic image synthesis. It applies light transport algorithms grounded in physics, providing a reproducible platform for evaluating materials, illumination, and camera models. To illustrate the structure of PBRT scene descriptions, we present a representative example. The configuration includes a perspective camera, two light sources (an infinite area light and a blackbody-based distant light), three spheres with distinct surface properties (diffuse, conducting, and dielectric), and a textured ground plane. Listing 1 presents the complete scene description in PBRT syntax, and Table 1 summarizes the function of each code block. Listing 1: PBRT scene configuration. 1LookAt 080# eye 20 .5 0 # look at point 3001 # up vector 4Camera "perspective" 5"float fov" [25] 6Sampler "halton" 7"integer pixelsamples" [2048] 8Integrator "volpath" 9Film "rgb" 10 "string filename" "sphere_sample.png" 11 "integer xresolution" [700] 12 "integer yresolution" [400] 13 ColorSpace "srgb" 14 WorldBegin 15 LightSource "infinite" 16 "rgb L" [0.4 0.45 0.5] 17 LightSource "distant" "float scale" [1.5] 18 "point3 from" [-30 40 100] 19 "blackbody L" [3000] 20 # --- GEOMETRY AND MATERIALS --- 21 # Sphere A: Diffuse Reflectance (RGB) 22 AttributeBegin 23 Translate -2 0.5 0 24 Material "diffuse" 25 "rgb reflectance" [0.8 0.2 0.2] # Red high reflectance 26 Shape "sphere" 27 "float radius" [0.5] 28 AttributeEnd 29 # Sphere B: Anisotropic Roughness (Conductor) 30 AttributeBegin 31 Translate 0 0.5 0 32 Material "conductor" 33 "rgb eta" [0.2 0.2 1.4] 34 "rgb k" [3.9 2.4 2.5] 35 "float uroughness" [0.1] 36 "float vroughness" [0.5] 37 "bool remaproughness" [true] 38 Shape "sphere" 39 "float radius" [0.5] 40 AttributeEnd 41 # Sphere C: Dielectric (Index of Refraction) 1 42 AttributeBegin 43 Translate 2 0.5 0 44 Material "dielectric" 45 "float eta" [1.5] # Index of Refraction 46 Shape "sphere" 47 "float radius" [0.5] 48 AttributeEnd 49 # Ground plane with checkerboard texture 50 AttributeBegin 51 Texture "checks" "spectrum" "checkerboard" 52 "float uscale" [16] 53 "float vscale" [16] 54 "rgb tex1" [0.1 0.1 0.1] 55 "rgb tex2" [0.8 0.8 0.8] 56 Material "diffuse" 57 "texture reflectance" "checks" 58 Translate 0 0 -1 59 Shape "bilinearmesh" 60 "point3 P" [ -20 -20 0 20 -20 0 -20 20 0 20 20 0 ] 61 "point2 uv" [0010 01 11] 62 AttributeEnd Table 1: Explanation of the PBRT scene description in Listing 1. Lines Explanation 1–3 Camera setup using LookAt: defines the eye position (0,8,0), the look-at point (0,0.5,0), and the up vector (0,0,1). 4–5 Perspective camera with a 25◦field of view. 6–7 Halton sampler with 2048 pixel samples. 8 Volumetric path-tracing integrator. 9–12 Film block: RGB film, output file sphere sample.png, resolution 700 ×400 pixels. 13 Color space: sRGB. 14 WorldBegin: start of scene geometry and lighting. 15–16 Infinite light source with grayish-blue spectrum [0.4,0.45,0.5]. 17–19 Distant light source at (–30,40,100), intensity scaled by 1.5, spectrum defined by a 3000 K blackbody. 22–28 Sphere A: diffuse red Lambertian material, translated to (–2,0.5,0), radius 0.5. 30–40 Sphere B: anisotropic conductor. Material defined by refractive indices η= [0.2,0.2,1.4] and extinction coefficients k= [3.9,2.4,2.5]. Roughness is anisotropic with u= 0.1, v= 0.5. Sphere at (0,0.5,0), radius 0.5. 42–48 Sphere C: dielectric sphere (transparent). Index of refraction η= 1.5, translated to (2,0.5,0), radius 0.5. 50–62 Ground plane: bilinear mesh with checkerboard texture. The texture alternates between dark gray [0.1,0.1,0.1] and light gray [0.8,0.8,0.8], repeated 16×16 across the plane. 2 2 Optimized Colour Space Transformation Matrices Algorithm 1 was applied to compute the optimized transformations from CIE XYZ to RGB for the four colour spaces implemented in PBRT. For each space, we present the optimized transformation matrix T∗ XY Z→RGB , as defined in Eq. (3) of the main document (see also Algorithm 1), together with the perceptual similarity metric M(IR, IS(µ)) defined in Eq. (9). The figures compare the spectral reference rendering with its corresponding optimized synthetic counterpart. sRGB The optimized transformation is T∗ XY Z→sRGB =  0.025763 −0.012221 −0.003964 −0.009648 0.018673 0.000414 0.000575 −0.002107 0.010917  . The resulting similarity metric is M(IR, IS(µ)) = 0.77. Reference sRGB: IR(SPD) Synthetic optimized sRGB: IS(µ) Rec.2020 The optimized transformation is T∗ XY Z→Rec.2020 =  0.015744 −0.003262 −0.002324 −0.007121 0.017266 0.000168 0.000208 −0.000505 0.011132  . The resulting similarity metric is M(IR, IS(µ)) = 2.06. Reference Rec.2020: IR(SPD) Synthetic optimized Rec.2020: IS(µ) 3 DCI-P3 The optimized transformation is T∗ XY Z→DCI-P3 =  0.022362 −0.008353 −0.003612 −0.008696 0.018478 0.000248 0.000387 −0.000822 0.010329  . The resulting similarity metric is M(IR, IS(µ)) = 1.57. Reference DCI-P3: IR(SPD) Synthetic optimized DCI-P3: IS(µ) ACES2065-1 The optimized transformation is T∗ XY Z→ACES2065-1 =  0.010284 0.000000 −0.000001 −0.005263 0.014574 0.001043 0.000000 0.000000 0.010831  . The resulting similarity metric is M(IR, IS(µ)) = 2.09. Reference ACES2065-1: IR(SPD) Synthetic optimized ACES2065-1: IS(µ) 4 3 Experimental Results To validate the proposed methodology, a psychometric test was conducted in which participants compared real and virtual scenes rendered using the PBRT system. The evaluation focused on three main aspects: material appearance, realism of illumination, and overall fidelity of the rendered scene relative to its real-world counterpart. Participants answered a series of structured questions using a five-point Likert scale, where 1 corresponded to the lowest agreement and 5 to the highest. The full set of evaluation questions is presented in Table 2. To analyze the responses, the percentage of selections for each of the five response options in every question was assigned a weight W(from 1 to 5). These weighted values were then used to compute a weighted score (W S) per option. For example, consider option 5 of question Q2in Table 2. It was selected by 39.1% of participants, resulting in a weighted score of 0.391×5 = 1.96. The final score for each question is obtained by summing the weighted contributions of all response options, with a maximum possible value of 5. For the same question Q2, the calculation yields 0 + 0.09 + 0.78 + 1.22 + 1.96 = 4.04. Table 2: Post-test survey on Visual Realism and Presence: detailed responses with weighted scores (W S) and final scores. Question Answer Options (Vote%, W S) Final Score Q1: How present did you feel in the virtual scene? (1) Not present: 0%, W S = 0 (2) Slightly present: 0%, W S = 0 (3) Moderately present: 0%, W S = 0 (4) Quite present: 48%, W S = 1.91 (5) Totally present: 52%, W S = 2.61 4.52 Q2: How would you rate the realism of the scene? (1) Unrealistic: 0%, W S = 0 (2) Somewhat realistic: 4.3%, W S = 0.09 (3) Average realism: 26.1%, W S = 0.78 (4) Mostly realistic: 30.4%, W S = 1.22 (5) Extremely realistic: 39.1%, W S = 1.96 4.04 Q3: How well did you perceive depth in the scene? (1) No depth: 0%, W S = 0 (2) Very little depth: 0%, W S = 0 (3) Moderate: 4.3%, W S = 0.13 (4) Quite a bit: 39.1%, W S = 1.56 (5) Highly perceptible: 56.5%, W S = 2.83 4.52 Q4: How comfortable did you feel? (1) Very uncomfortable: 0%, W S = 0 (2) Uncomfortable: 0%, W S = 0 (3) Neutral: 0%, W S = 0 (4) Comfortable: 34.8%, W S = 1.39 (5) Very comfortable: 65.2%, W S = 3.26 4.65 Q5: How clear and sharp was the scene? (1) Very blurry: 0%, W S = 0 (2) Blurry: 0%, W S = 0 (3) Neutral: 17.4%, W S = 0.52 (4) Clear: 39.1%, W S = 1.56 (5) Very clear: 43.5%, W S = 2.18 4.26 5 Table 3: Post-test survey on Lighting and Spatial Perception: detailed responses with weighted scores (W S) and final scores. Question Answer Options (Vote%, W S) Final Score Q6: How open or limited was the scene? (1) Very confined: 0%, W S = 0 (2) Somewhat limited: 26%, W S = 0.52 (3) Neutral: 9%, W S = 0.26 (4) Fairly open: 61%, W S = 2.40 (5) Completely open: 4%, W S = 0.22 3.43 Q7: Perception of colour temperature change? (1) No change: 0%, W S = 0 (2) Too warm: 13%, W S = 0.26 (3) Too cool: 4%, W S = 0.13 (4) Slight change: 0%, W S = 0 (5) Appropriate: 83%, W S = 4.13 4.52 Q8: How comfortable was the scene? (1) Not at all: 0%, W S = 0 (2) Slightly: 0%, W S = 0 (3) Somewhat: 13%, W S = 0.39 (4) Quite: 65%, W S = 2.61 (5) Extremely: 22%, W S = 1.09 4.08 Q9: How did you perceive the lighting? (1) Very glaring: 0%, W S = 0 (2) Glaring: 0%, W S = 0 (3) Moderate: 4%, W S = 0.13 (4) Soft: 70%, W S = 2.78 (5) Very soft: 26%, W S = 1.31 4.22 Table 4: Post-test survey on Lighting and Spatial Perception: detailed responses with weighted scores (W S) and final scores. Question Answer Options (Vote%, W S) Final Score Q10: Brightness of the scene? (1) Too bright: 0%, W S = 0 (2) Too dark: 0%, W S = 0 (3) Slightly intense: 0%, W S = 0 (4) Balanced: 74%, W S = 2.96 (5) Soft: 26%, W S = 1.31 4.26 Q11: Pleasantness of experience? (1) Very unpleasant: 0%, W S = 0 (2) Unpleasant: 0%, W S = 0 (3) Neutral: 0%, W S = 0 (4) Pleasant: 30%, W S = 1.22 (5) Very pleasant: 70%, W S = 3.48 4.70 Q12: How alert or sleepy were you? (1) Very sleepy: 0%, W S = 0 (2) Somewhat sleepy: 13%, W S = 0.26 (3) Neutral: 9%, W S = 0.26 (4) Quite alert: 26%, W S = 1.04 (5) Very alert: 52%, W S = 2.61 4.18 Q13: How free or restricted did you feel? (1) Completely restricted: 0%, W S = 0 (2) Some restrictions: 22%, W S = 0.43 (3) Neutral: 13%, W S = 0.39 (4) Fairly free: 61%, W S = 2.44 (5) Completely free: 4%, W S = 0.22 3.48 Q14: How noisy or quiet was it? (1) Very noisy: 0%, W S = 0 (2) Noisy: 0%, W S = 0 (3) Neutral: 4%, W S = 0.13 (4) Quiet: 30%, W S = 1.22 (5) Very quiet: 65%, W S = 3.26 4.61 Q15: How relaxed or nervous did you feel? (1) Very nervous: 0%, W S = 0 (2) Slightly: 4%, W S = 0.09 (3) Neutral: 26%, W S = 0.78 (4) Somewhat relaxed: 22%, W S = 0.87 (5) Very relaxed: 48%, W S = 2.39 4.13 Q16: Overall satisfaction? (1) Very dissatisfied: 0%, W S = 0 (2) Dissatisfied: 0%, W S = 0 (3) Neutral: 0%, W S = 0 (4) Satisfied: 22%, W S = 0.87 (5) Very satisfied: 78%, W S = 3.92 4.78 6