Add more LK notes

shaders/cMotionBlur.fx

@@ -346,7 +346,7 @@ namespace MotionBlur
     float2 Lucas_Kanade(int Level, float2 Vectors, float4 TexCoord)
     {
         /*
-            Fetch 2x2 bilinear-filtered windows for spatial and temporal dertivatives
+            Fetch 2x2 bilinear-filtered windows for spatial(S) and temporal(T) dertivatives
             [TexCoord.xw TexCoord.zw]
             [TexCoord.xy TexCoord.zy]
         */
@@ -375,36 +375,39 @@ namespace MotionBlur
             B2 = IyIt
         */
 
-        // Solve window equation at matrix A
+        // Create matrix A and solve its window sum
         // 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]);
-
         // 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
+        // Create -IxIy (A12) for A^-1 and its determinant
         A.z = A.z * (-1.0);
 
-        // Calculate determinant
+        // Calculate A^-1 determinant
         float D = ((A.x * A.y) - (A.z * A.z));
 
+        // Calculate A^-1
+        A = (1.0 / D) * A;
+
+        // Create vector B and solve its window sum
+        // 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]);
+
         // 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;
+        LK = (D != 0.0) ? LK + Vectors : 0.0;
         return LK;
     }
 

shaders/cOpticalFlowLK.fx

@@ -368,36 +368,39 @@ namespace OpticalFlowLK
             B2 = IyIt
         */
 
-        // Solve window equation at matrix A
+        // Create matrix A and solve its window sum
         // 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]);
-
         // 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
+        // Create -IxIy (A12) for A^-1 and its determinant
         A.z = A.z * (-1.0);
 
-        // Calculate determinant
+        // Calculate A^-1 determinant
         float D = ((A.x * A.y) - (A.z * A.z));
 
+        // Calculate A^-1
+        A = (1.0 / D) * A;
+
+        // Create vector B and solve its window sum
+        // 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]);
+
         // 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;
+        LK = (D != 0.0) ? LK + Vectors : 0.0;
         return LK;
     }
 

shaders/kDatamosh.fx

@@ -440,36 +440,39 @@ namespace Datamosh
             B2 = IyIt
         */
 
-        // Solve window equation at matrix A
+        // Create matrix A and solve its window sum
         // 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]);
-
         // 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
+        // Create -IxIy (A12) for A^-1 and its determinant
         A.z = A.z * (-1.0);
 
-        // Calculate determinant
+        // Calculate A^-1 determinant
         float D = ((A.x * A.y) - (A.z * A.z));
 
+        // Calculate A^-1
+        A = (1.0 / D) * A;
+
+        // Create vector B and solve its window sum
+        // 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]);
+
         // 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;
+        LK = (D != 0.0) ? LK + Vectors : 0.0;
         return LK;
     }