Skip to content

Commit

Permalink
Document LK
Browse files Browse the repository at this point in the history
  • Loading branch information
brimson committed Jul 22, 2022
1 parent 42c6c84 commit c13a9fe
Show file tree
Hide file tree
Showing 3 changed files with 129 additions and 66 deletions.
65 changes: 43 additions & 22 deletions shaders/cMotionBlur.fx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -345,46 +345,67 @@ namespace MotionBlur

float2 Lucas_Kanade(int Level, float2 Vectors, float4 TexCoord)
{
// 3x3 Spatial derivative window in 4 bilinear fetches
// [TexCoord.xw TexCoord.zw]
// [TexCoord.xy TexCoord.zy]
/*
Fetch 2x2 bilinear-filtered windows for spatial and temporal dertivatives
[TexCoord.xw TexCoord.zw]
[TexCoord.xy TexCoord.zy]
*/

float2 S[4];
S[0] = tex2D(Sample_Common_1_A, TexCoord.xw).xy;
S[1] = tex2D(Sample_Common_1_A, TexCoord.zw).xy;
S[2] = tex2D(Sample_Common_1_A, TexCoord.xy).xy;
S[3] = tex2D(Sample_Common_1_A, TexCoord.zy).xy;

// A.x = Ix^2 (A11); A.y = Iy^2 (A22); A.z = IxIy (A12)
float3 A = 0.0;
A += (S[0].xyx * S[0].xyy);
A += (S[1].xyx * S[1].xyy);
A += (S[2].xyx * S[2].xyy);
A += (S[3].xyx * S[3].xyy);
A.xy = max(A.xy, FP16_SMALLEST_SUBNORMAL);
A.z = A.z * (-1.0);

// Determinant
float D = ((A.x * A.y) - (A.z * A.z));

// 3x3 Temporal derivative window in 4 bilinear fetches
float T[4];
T[0] = tex2D(Sample_Common_1_B, TexCoord.xw).x;
T[1] = tex2D(Sample_Common_1_B, TexCoord.zw).x;
T[2] = tex2D(Sample_Common_1_B, TexCoord.xy).x;
T[3] = tex2D(Sample_Common_1_B, TexCoord.zy).x;

// B.x = IxIt (Q1); B.y = IyIt (Q2)
/*
Calculate Lucas-Kanade optical flow by solving (A^-1 * B)
[A11 A12]^-1 [-B1] -> [ A11 -A12] [-B1]
[A21 A22]^-1 [-B2] -> [-A21 A22] [-B2]
A11 = Ix^2
A12 = IxIy
A21 = IxIy
A22 = Iy^2
B1 = IxIt
B2 = IyIt
*/

// Solve window equation at matrix A
// A.x = A11; A.y = A22; A.z = A12/A22
float3 A = 0.0;
A += (S[0].xyx * S[0].xyy);
A += (S[1].xyx * S[1].xyy);
A += (S[2].xyx * S[2].xyy);
A += (S[3].xyx * S[3].xyy);

// Solve window equation at vector B
// B.x = B1; B.y = B2
float2 B = 0.0;
B += (S[0] * T[0]);
B += (S[1] * T[1]);
B += (S[2] * T[2]);
B += (S[3] * T[3]);

float2 UV = 0.0;
UV.x = dot(A.yz, -B.xy);
UV.y = dot(A.zx, -B.xy);
UV = (D != 0.0) ? (UV / D) + Vectors : 0.0;
return UV;
// Ensure Lucas-Kanade's determinant is non-zero
A.xy = max(A.xy, FP16_SMALLEST_SUBNORMAL);

// Create -IxIy (A12) for A's determinant and LK matrix
A.z = A.z * (-1.0);

// Calculate determinant
float D = ((A.x * A.y) - (A.z * A.z));

// Calculate Lucas-Kanade matrix
float2 LK = 0.0;
LK.x = dot(A.yz, -B.xy);
LK.y = dot(A.zx, -B.xy);
LK = (D != 0.0) ? (LK / D) + Vectors : 0.0;
return LK;
}

float2 Average2D(sampler2D Source, float4 TexCoord)
Expand Down
65 changes: 43 additions & 22 deletions shaders/cOpticalFlowLK.fx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -338,46 +338,67 @@ namespace OpticalFlowLK

float2 Lucas_Kanade(int Level, float2 Vectors, float4 TexCoord)
{
// 3x3 Spatial derivative window in 4 bilinear fetches
// [TexCoord.xw TexCoord.zw]
// [TexCoord.xy TexCoord.zy]
/*
Fetch 2x2 bilinear-filtered windows for spatial and temporal dertivatives
[TexCoord.xw TexCoord.zw]
[TexCoord.xy TexCoord.zy]
*/

float2 S[4];
S[0] = tex2D(Sample_Common_1_A, TexCoord.xw).xy;
S[1] = tex2D(Sample_Common_1_A, TexCoord.zw).xy;
S[2] = tex2D(Sample_Common_1_A, TexCoord.xy).xy;
S[3] = tex2D(Sample_Common_1_A, TexCoord.zy).xy;

// A.x = Ix^2 (A11); A.y = Iy^2 (A22); A.z = IxIy (A12)
float3 A = 0.0;
A += (S[0].xyx * S[0].xyy);
A += (S[1].xyx * S[1].xyy);
A += (S[2].xyx * S[2].xyy);
A += (S[3].xyx * S[3].xyy);
A.xy = max(A.xy, FP16_SMALLEST_SUBNORMAL);
A.z = A.z * (-1.0);

// Determinant
float D = ((A.x * A.y) - (A.z * A.z));

// 3x3 Temporal derivative window in 4 bilinear fetches
float T[4];
T[0] = tex2D(Sample_Common_1_B, TexCoord.xw).x;
T[1] = tex2D(Sample_Common_1_B, TexCoord.zw).x;
T[2] = tex2D(Sample_Common_1_B, TexCoord.xy).x;
T[3] = tex2D(Sample_Common_1_B, TexCoord.zy).x;

// B.x = IxIt (Q1); B.y = IyIt (Q2)
/*
Calculate Lucas-Kanade optical flow by solving (A^-1 * B)
[A11 A12]^-1 [-B1] -> [ A11 -A12] [-B1]
[A21 A22]^-1 [-B2] -> [-A21 A22] [-B2]
A11 = Ix^2
A12 = IxIy
A21 = IxIy
A22 = Iy^2
B1 = IxIt
B2 = IyIt
*/

// Solve window equation at matrix A
// A.x = A11; A.y = A22; A.z = A12/A22
float3 A = 0.0;
A += (S[0].xyx * S[0].xyy);
A += (S[1].xyx * S[1].xyy);
A += (S[2].xyx * S[2].xyy);
A += (S[3].xyx * S[3].xyy);

// Solve window equation at vector B
// B.x = B1; B.y = B2
float2 B = 0.0;
B += (S[0] * T[0]);
B += (S[1] * T[1]);
B += (S[2] * T[2]);
B += (S[3] * T[3]);

float2 UV = 0.0;
UV.x = dot(A.yz, -B.xy);
UV.y = dot(A.zx, -B.xy);
UV = (D != 0.0) ? (UV / D) + Vectors : 0.0;
return UV;
// Ensure Lucas-Kanade's determinant is non-zero
A.xy = max(A.xy, FP16_SMALLEST_SUBNORMAL);

// Create -IxIy (A12) for A's determinant and LK matrix
A.z = A.z * (-1.0);

// Calculate determinant
float D = ((A.x * A.y) - (A.z * A.z));

// Calculate Lucas-Kanade matrix
float2 LK = 0.0;
LK.x = dot(A.yz, -B.xy);
LK.y = dot(A.zx, -B.xy);
LK = (D != 0.0) ? (LK / D) + Vectors : 0.0;
return LK;
}

float2 Average2D(sampler2D Source, float4 TexCoord)
Expand Down
65 changes: 43 additions & 22 deletions shaders/kDatamosh.fx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -410,46 +410,67 @@ namespace Datamosh

float2 Lucas_Kanade(int Level, float2 Vectors, float4 TexCoord)
{
// 3x3 Spatial derivative window in 4 bilinear fetches
// [TexCoord.xw TexCoord.zw]
// [TexCoord.xy TexCoord.zy]
/*
Fetch 2x2 bilinear-filtered windows for spatial and temporal dertivatives
[TexCoord.xw TexCoord.zw]
[TexCoord.xy TexCoord.zy]
*/

float2 S[4];
S[0] = tex2D(Sample_Common_1_A, TexCoord.xw).xy;
S[1] = tex2D(Sample_Common_1_A, TexCoord.zw).xy;
S[2] = tex2D(Sample_Common_1_A, TexCoord.xy).xy;
S[3] = tex2D(Sample_Common_1_A, TexCoord.zy).xy;

// A.x = Ix^2 (A11); A.y = Iy^2 (A22); A.z = IxIy (A12)
float3 A = 0.0;
A += (S[0].xyx * S[0].xyy);
A += (S[1].xyx * S[1].xyy);
A += (S[2].xyx * S[2].xyy);
A += (S[3].xyx * S[3].xyy);
A.xy = max(A.xy, FP16_SMALLEST_SUBNORMAL);
A.z = A.z * (-1.0);

// Determinant
float D = ((A.x * A.y) - (A.z * A.z));

// 3x3 Temporal derivative window in 4 bilinear fetches
float T[4];
T[0] = tex2D(Sample_Common_1_B, TexCoord.xw).x;
T[1] = tex2D(Sample_Common_1_B, TexCoord.zw).x;
T[2] = tex2D(Sample_Common_1_B, TexCoord.xy).x;
T[3] = tex2D(Sample_Common_1_B, TexCoord.zy).x;

// B.x = IxIt (Q1); B.y = IyIt (Q2)
/*
Calculate Lucas-Kanade optical flow by solving (A^-1 * B)
[A11 A12]^-1 [-B1] -> [ A11 -A12] [-B1]
[A21 A22]^-1 [-B2] -> [-A21 A22] [-B2]
A11 = Ix^2
A12 = IxIy
A21 = IxIy
A22 = Iy^2
B1 = IxIt
B2 = IyIt
*/

// Solve window equation at matrix A
// A.x = A11; A.y = A22; A.z = A12/A22
float3 A = 0.0;
A += (S[0].xyx * S[0].xyy);
A += (S[1].xyx * S[1].xyy);
A += (S[2].xyx * S[2].xyy);
A += (S[3].xyx * S[3].xyy);

// Solve window equation at vector B
// B.x = B1; B.y = B2
float2 B = 0.0;
B += (S[0] * T[0]);
B += (S[1] * T[1]);
B += (S[2] * T[2]);
B += (S[3] * T[3]);

float2 UV = 0.0;
UV.x = dot(A.yz, -B.xy);
UV.y = dot(A.zx, -B.xy);
UV = (D != 0.0) ? (UV / D) + Vectors : 0.0;
return UV;
// Ensure Lucas-Kanade's determinant is non-zero
A.xy = max(A.xy, FP16_SMALLEST_SUBNORMAL);

// Create -IxIy (A12) for A's determinant and LK matrix
A.z = A.z * (-1.0);

// Calculate determinant
float D = ((A.x * A.y) - (A.z * A.z));

// Calculate Lucas-Kanade matrix
float2 LK = 0.0;
LK.x = dot(A.yz, -B.xy);
LK.y = dot(A.zx, -B.xy);
LK = (D != 0.0) ? (LK / D) + Vectors : 0.0;
return LK;
}

float2 Average2D(sampler2D Source, float4 TexCoord)
Expand Down

0 comments on commit c13a9fe

Please sign in to comment.