Anisotropic texture filtering using weights of an anisotropic filter that minimize a cost function
A method of performing anisotropic texture filtering includes generating one or more parameters describing an elliptical footprint in texture space; performing isotropic filtering at each sampling point of a set of sampling points in an ellipse to be sampled to produce a plurality of isotropic filter results, the ellipse to be sampled based on the elliptical footprint; selecting, based on one or more parameters of the set of sampling points and one or more parameters of the ellipse to be sampled, weights of an anisotropic filter that minimize a cost function that penalises high frequencies in the filter response of the anisotropic filter under a constraint that the variance of the anisotropic filter is related to an anisotropic ratio squared, the anisotropic ratio being the ratio of a major radius of the ellipse to be sampled and a minor axis of the ellipse to be sampled; and combining the plurality of isotropic filter results using the selected weights of the anisotropic filter to generate at least a portion of a filter result.
1. A method of performing anisotropic texture filtering, the method comprising:
generating one or more parameters describing an elliptical footprint in texture space;
performing isotropic filtering at each sampling point of a set of sampling points in an ellipse to be sampled to produce a plurality of isotropic filter results, the ellipse to be sampled based on the elliptical footprint;
selecting, based on one or more parameters of the set of sampling points and one or more parameters of the ellipse to be sampled, weights of an anisotropic filter that minimize a cost function that penalises high frequencies in the filter response of the anisotropic filter under a constraint that the variance of the anisotropic filter is related to an anisotropic ratio squared, the anisotropic ratio being the ratio of a major radius of the ellipse to be sampled and a minor axis of the ellipse to be sampled; and
combining the plurality of isotropic filter results using the selected weights of the anisotropic filter to generate at least a portion of a filter result.
2. The method of claim 1 , wherein the anisotropic filter is representable as the absolute value squared of a first function, and the cost function is a product of the modulus squared spatial and spectral variances of the first function.
3. The method of claim 2 , wherein the cost function is
η
∫
-
∞
+
∞
dx
❘
"\[LeftBracketingBar]"
(
ϕ
′
(
x
)
❘
"\[RightBracketingBar]"
2
,
where η is the anisotropic ratio, ϕ(x) is the first function, ϕ′(x) is the derivative of ϕ(x) with respect to x, and x represents a position in texture space with respect to a midpoint of the major axis of the elliptical footprint.
4. The method of claim 2 , wherein the cost function is
∑
n
∈
S
❘
"\[LeftBracketingBar]"
ϕ
n
+
1
-
ϕ
n
❘
"\[RightBracketingBar]"
2
+
∑
n
∈
S
❘
"\[LeftBracketingBar]"
ϕ
n
-
ϕ
n
-
1
❘
"\[RightBracketingBar]"
2
,
S is the set of sampling points, ϕ is the first function and n∉S⇒ϕ n =0.
5. The method of claim 1 , wherein the cost function is a function representing the Euclidean norm of the anisotropic filter.
6. The method of claim 5 , wherein the anisotropic filter is representable as the absolute value squared of a first function ϕ(x), the cost function is
∫
-
∞
+
∞
dx
❘
"\[LeftBracketingBar]"
ϕ
(
x
)
❘
"\[RightBracketingBar]"
4
,
and x represents a position in texture space with respect to a midpoint of the major axis of the elliptical footprint.
7. The method of claim 5 , wherein the anisotropic filter is representable as the absolute value squared of a first function ϕ, and the cost function is Σ n∈S |ϕ n | 4 wherein S is the set of sampling points and n∉S⇒ϕ n =0.
8. The method of claim 1 , wherein the cost function is a function representing a spectral spread of the anisotropic filter.
9. The method of claim 8 , wherein the anisotropic filter is representable as the absolute value squared of a first function ϕ(x), the cost function is
∫
-
∞
+
∞
dx
❘
"\[LeftBracketingBar]"
ϕ
′
(
x
)
ϕ
(
x
)
❘
"\[RightBracketingBar]"
2
,
ϕ′(x) is the derivative of ϕ(x) with respect to x, and x represents a position in texture space with respect to a midpoint of the major axis of the elliptical footprint.
10. The method of claim 8 , wherein the anisotropic filter is representable as the absolute value squared of a first function ϕ, the cost function is
∑
n
∈
S
❘
"\[LeftBracketingBar]"
(
ϕ
n
+
1
-
ϕ
n
)
ϕ
n
❘
"\[RightBracketingBar]"
2
+
∑
n
∈
S
❘
"\[LeftBracketingBar]"
(
ϕ
n
-
ϕ
n
-
1
)
ϕ
n
❘
"\[RightBracketingBar]"
2
,
S is the set of sampling points and n∉S⇒ϕ n =0.
11. The method of claim 1 , wherein the sampling points of the set of sampling points lie along a major axis of the elliptical footprint.
12. The method of claim 1 , wherein the one or more parameters of the ellipse to be sampled comprises the anisotropic ratio of the ellipse to be sampled.
13. The method of claim 1 , wherein the one or more parameters of the set of sampling points comprises a number of sampling points in the set of sampling points, an offset of a first sampling point from a middle point of the major radius of the elliptical footprint, and a spacing between adjacent sampling points in the set of sampling points in the texture space.
14. The method of claim 1 , wherein selecting the weights of the anisotropic filter that minimize a cost function that penalises high frequencies in the filter response of the anisotropic filter under a constraint that the variance of the anisotropic filter is related to an anisotropic ratio squared comprises selecting a set of weights from a lookup table based on the one or more parameters of the set of sampling points and the one or more parameters of the ellipse to be sampled, the lookup table comprising weights that minimize the cost function for a plurality of values for the parameters.
15. The method of claim 1 , wherein a number of sampling points in the set of sampling points is greater than two, and a spacing between adjacent sampling points in the set of sampling points is proportional to √{square root over (1−η −2 )} units, wherein η is the anisotropic ratio and a unit corresponds to the minor radius of the ellipse to be sampled.
16. The method of claim 1 , wherein the weights of the anisotropic filter are further selected under a constraint that the anisotropic filter has a mean of zero and/or the anisotropic filter is normalised to one.
17. The method of claim 1 , wherein the set of sampling points comprises N sampling points and N is proportional to the anisotropic ratio.
18. A method of generating an image, the method comprising performing the method as set forth in claim 1 , and generating an image based on the at least a portion of the filter result.
19. A texture filtering unit for use in a graphics processing system, the texture filtering unit configured to perform the method as set forth in claim 1 .
20. A non-transitory computer readable storage medium having stored thereon computer readable instructions that, when executed at a computer system, cause the computer system to perform the method as set forth in claim 1 .