Úvod do vzhledu materiálů

ANI-PG2 · přednáška 01

Jiří Filip · ÚTIA AV ČR

Material appearance is part of how we understand the world.

• Visual scene analysis, scene segmentation and image retrieval.
• Movie and game industry; cultural heritage digitization and interior design.
• Visual safety simulation, visual psychophysics and medical image analysis.

• Geometry describes the shape.
• Lighting determines the incident illumination.
• Material appearance determines the light–material interaction.

The general model connects incoming and outgoing positions and directions, time and wavelength.

Source notation includes a 16-dimensional general reflectance function. The complete equation and its diagram remain in the source illustration.

• BSSRDF: scattering may involve different entry and exit positions.
• BTF: directional appearance of a textured material.
• BRDF: directional reflection for a local opaque surface model.

• Texture and multispectral/dynamic texture.
• Isotropic BRDF, BRDF, BTDF and BSDF for homogeneous materials.
• Spatially varying BRDF, BTF, surface light field and surface reflectance field.
• Reflectance fields / BSSRDF.

• BSSRDF: 9D in the source convention.
• BTF / SVBRDF: 7D in the source convention.
• BRTTF: 9D in the source convention.

• SRF and SLF: 5D in the source convention.
• Multispectral / dynamic texture: 3/4D in the source convention.

• BSDF: 7D; anisotropic BTDF: 5D.
• Anisotropic BRDF: 5D; isotropic BRDF: 4D.

Compare BRDF, BSDF, BTF, BTDF and BSSRDF through the author’s examples.

Total outgoing radiance consists of emitted and reflected radiance:

L_o(x, ω_o) = L_e(x, ω_o) + L_r(x, ω_o)

L_r(x, ω_o) = ∫_Ω⁺ f_r(x, ω_i, ω_o) L_i(x, ω_i) (n · ω_i) dω_i

Surface reflectance × incident illumination × projected area, integrated over incoming directions.

• Global illumination: ray tracing approaches.
• Approximation by a set of point lights.

• Irradiance E = dΦ / dA, in W m⁻².
• Radiance L = d²Φ / (dA cos θ dω), in W m⁻² sr⁻¹.
• BRDF fᵣ = dLₒ / dEᵢ, in sr⁻¹.
• Directional albedo integrates reflected energy over outgoing directions.
• Mean albedo averages directional albedo over incident directions.

• Helmholtz reciprocity: fᵣ(ωᵢ, ωₒ) = fᵣ(ωₒ, ωᵢ).
• Energy conservation: ∫Ω⁺ fᵣ(ωᵢ, ωₒ) cos θₒ dωₒ ≤ 1.
• Isotropy: invariance to simultaneous rotation of the incoming and outgoing directions around the normal.

f_r(ω_i, ω_o) = dL_o(ω_o) / dE_i(ω_i)

• Source/sensor direction reciprocity.
• Energy conservation: reflected fraction between 0 and 1.
• Non-negativity.

• Reflectance depends on illumination and viewing directions.
• Isotropic BRDF uses the azimuth difference.
• Anisotropic appearance also depends on material orientation.

• BTF is a texture dependent on illumination and viewing directions.
• Captures inter-reflections, subsurface scattering, local masking and shadowing.
• Thousands of images per material; data may occupy gigabytes.
• Compression and modelling are necessary.

The source shows a fabric sample and its directional appearance on a rendered shape.

Compare the author’s rendered examples. BTF retains spatial and angular effects that a homogeneous BRDF cannot describe.

• Captured spatial/angular reflectance → pixel-wise apparent BRDF.
• Estimate SVBRDF / PBR parameter maps.
• The diagram presents decreasing storage size and visual fidelity along this approximation pipeline.

• Rough structures create pixel-wise misalignment between different views.
• Occlusion changes which surface detail is visible.
• The source proposes processing individual views separately.

A pixel’s apparent reflectance includes visibility and structure effects. The author contrasts homogeneous BRDF samples with spatially varying measured appearance.

• Restrictions: opaque surfaces, no subsurface scattering.
• Nearly flat surfaces: no occlusion/masking and no interaction between pixels.
• Simpler local transport allows spatial clustering and sparse measurements.
• Examples: lacquered wood and wallpaper.

Subsurface transport matters: the source shows light spreading in a semitransparent object.

Directional fibres, weaving patterns and surface finishing change appearance with orientation.

The author’s example illustrates a strongly directional highlight on a rendered draped surface.

Fine structure and directional highlights interact. The source compares three appearances of the same object.

The source illustration shows a narrow highlight and spatially structured appearance on elongated objects.

Small bright features create sparkle. Compare the source’s appearance examples.

Compare photographs with a measured and rendered BTF. Colour changes with illumination/view configuration.

Material appearance can combine spatial structure, specularity, anisotropy, transmission and colour shifts.