US 12,444,123 B2
Method of using a bi-directional texture function
Benjamin Lanfer, Münster (DE); Philipp Reisloh, Münster (DE); Mark Gutjahr, Münster (DE); Florina Trost, Münster (DE); Weiran Lu, Münster (DE); and Jens Wegner, Münster (DE)
Assigned to BASF COATINGS GMBH, Muenster (DE)
Appl. No. 18/003,461
Filed by BASF COATINGS GMBH, Münster (DE)
PCT Filed Jun. 21, 2021, PCT No. PCT/EP2021/066887
§ 371(c)(1), (2) Date Dec. 27, 2022,
PCT Pub. No. WO2022/002676, PCT Pub. Date Jan. 6, 2022.
Claims priority of application No. 20182808 (EP), filed on Jun. 29, 2020.
Prior Publication US 2023/0316627 A1, Oct. 5, 2023
Int. Cl. G06T 15/04 (2011.01); G06T 15/50 (2011.01)
CPC G06T 15/04 (2013.01) [G06T 15/506 (2013.01)] 14 Claims
 
1. A method of using a bi-directional texture function (BTF) to simulate an object, the method comprising:
generating an optimized BTF by:
measuring an initial BTF for the object using a camera-based measurement device;
capturing spectral reflectance data for the object for a pre-given number of different measurement geometries using a spectrophotometer; and
adapting the initial BTF of formula (1) by segmenting

OG Complex Work Unit Math
with
x: surface coordinates of the sample/object,
l, ō: illumination and observation/viewing directions at a basecoat of the sample,
χ(l,ō): color table depending on illumination and observation direction
α: Albedo or diffuse reflectivity,
FSk,αk,Fo,kCT(l,ō): a k-th Cook-Torrance lobe, corresponding to a Bi-directional Reflectance Distribution Function (BRDF) that describes a glossiness of a microfacet surface,
Sk: weight for the k-th Cook-Torrance lobe,
αk: parameter for a Beckmann distribution of the k-th Cook-Torrance lobe,
F0,k: Fresnel reflectivity for the k-th Cook-Torrance lobe, and
Ξ(x,l,ō): table of spatial texture images depending on illumination and observation direction,
into a term;

OG Complex Work Unit Math
and a term Ξ(x,l,ō) (F2), further dividing the term (F1) into a first sub-term corresponding to the color table depending on illumination and observation direction χ(l,ō) and a second sub-term corresponding to an intensity function

OG Complex Work Unit Math
and minimizing a color difference between the captured spectral reflectance data and the initial BTF by optimizing in a first optimization step the parameters of the first sub-term while the parameters of the second sub-term are kept constant, and by optimizing in a second optimization step the parameters of the second sub-term while the parameters of the first sub-term are kept constant;
rendering the object or an optical appearance of the object using the optimized BTF, wherein the object is an automobile, a vehicle part, a piece of furniture, a piece of clothing, or a packaging material, said rendering comprising applying parameters of the optimized BTF to at least one texture function to reproduce optical properties including at least a color and spatially varying appearance of the object at a given illumination level, observation angle, and/or observation direction; and
displaying the rendered object or optical appearance of the object on a display.