Improve adjoint matching for fan/cone BP functions, and clean up

2 files changed, 139 insertions, 71 deletions

diff --git a/cuda/3d/cone_bp.cu b/cuda/3d/cone_bp.cu
index 2a7ec80..a614c29 100644
--- a/cuda/3d/cone_bp.cu
+++ b/cuda/3d/cone_bp.cu
@@ -55,7 +55,13 @@ static const unsigned int g_volBlockY = 32;
 
 static const unsigned g_MaxAngles = 1024;
 
-__constant__ float gC_C[12*g_MaxAngles];
+struct DevConeParams {
+	float4 fNumU;
+	float4 fNumV;
+	float4 fDen;
+};
+
+__constant__ DevConeParams gC_C[g_MaxAngles];
 
 bool bindProjDataTexture(const cudaArray* array)
 {
@@ -118,16 +124,13 @@ __global__ void dev_cone_BP(void* D_volData, unsigned int volPitch, int startAng
 
 		for (int angle = startAngle; angle < endAngle; ++angle, fAngle += 1.0f)
 		{
-			float4 fCu  = make_float4(gC_C[12*angle+0], gC_C[12*angle+1], gC_C[12*angle+2], gC_C[12*angle+3]);
-			float4 fCv  = make_float4(gC_C[12*angle+4], gC_C[12*angle+5], gC_C[12*angle+6], gC_C[12*angle+7]);
-			float4 fCd  = make_float4(gC_C[12*angle+8], gC_C[12*angle+9], gC_C[12*angle+10], gC_C[12*angle+11]);
+			float4 fCu  = gC_C[angle].fNumU;
+			float4 fCv  = gC_C[angle].fNumV;
+			float4 fCd  = gC_C[angle].fDen;
 
 			float fUNum = fCu.w + fX * fCu.x + fY * fCu.y + fZ * fCu.z;
 			float fVNum = fCv.w + fX * fCv.x + fY * fCv.y + fZ * fCv.z;
-			float fDen  = fCd.w + fX * fCd.x + fY * fCd.y + fZ * fCd.z;
-
-			// fCd.w = -|| u v s || (determinant of 3x3 matrix with cols u,v,s)
-			// fDen =  || u v (x-s) ||
+			float fDen  = (FDKWEIGHT ? 1.0f : fCd.w) + fX * fCd.x + fY * fCd.y + fZ * fCd.z;
 
 			float fU,fV, fr;
 
@@ -137,20 +140,7 @@ __global__ void dev_cone_BP(void* D_volData, unsigned int volPitch, int startAng
 				fU = fUNum * fr;
 				fV = fVNum * fr;
 				float fVal = tex3D(gT_coneProjTexture, fU, fAngle, fV);
-				if (FDKWEIGHT) {
-					// The correct factor here is this one:
-					// Z[idx] += (fr*fCd.w)*(fr*fCd.w)*fVal;
-					// This is the square of the magnification factor
-					// from fX,fY,fZ to the virtual detector, where the
-					// virtual detector is the plane through the origin
-					// parallel to the detector, so spanned by u,v.
-
-					// Since we are assuming we have a circular cone
-					// beam trajectory, fCd.w is constant, and we instead
-					// multiply by fCd.w*fCd.w in the FDK preweighting step.
-					Z[idx] += fr*fr*fVal;
-				} else
-					Z[idx] += fVal;
+				Z[idx] += fr*fr*fVal;
 
 				fUNum += fCu.z;
 				fVNum += fCv.z;
@@ -217,19 +207,9 @@ __global__ void dev_cone_BP_SS(void* D_volData, unsigned int volPitch, int start
 
 		for (int angle = startAngle; angle < endAngle; ++angle, fAngle += 1.0f)
 		{
-
-			const float fCux = gC_C[12*angle+0];
-			const float fCuy = gC_C[12*angle+1];
-			const float fCuz = gC_C[12*angle+2];
-			const float fCuc = gC_C[12*angle+3];
-			const float fCvx = gC_C[12*angle+4];
-			const float fCvy = gC_C[12*angle+5];
-			const float fCvz = gC_C[12*angle+6];
-			const float fCvc = gC_C[12*angle+7];
-			const float fCdx = gC_C[12*angle+8];
-			const float fCdy = gC_C[12*angle+9];
-			const float fCdz = gC_C[12*angle+10];
-			const float fCdc = gC_C[12*angle+11];
+			float4 fCu  = gC_C[angle].fNumU;
+			float4 fCv  = gC_C[angle].fNumV;
+			float4 fCd  = gC_C[angle].fDen;
 
 			float fXs = fX;
 			for (int iSubX = 0; iSubX < iRaysPerVoxelDim; ++iSubX) {
@@ -238,14 +218,15 @@ __global__ void dev_cone_BP_SS(void* D_volData, unsigned int volPitch, int start
 			float fZs = fZ;
 			for (int iSubZ = 0; iSubZ < iRaysPerVoxelDim; ++iSubZ) {
 
-				const float fUNum = fCuc + fXs * fCux + fYs * fCuy + fZs * fCuz;
-				const float fVNum = fCvc + fXs * fCvx + fYs * fCvy + fZs * fCvz;
-				const float fDen = fCdc + fXs * fCdx + fYs * fCdy + fZs * fCdz;
+				const float fUNum = fCu.w + fX * fCu.x + fY * fCu.y + fZ * fCu.z;
+				const float fVNum = fCv.w + fX * fCv.x + fY * fCv.y + fZ * fCv.z;
+				const float fDen  = fCd.w + fX * fCd.x + fY * fCd.y + fZ * fCd.z;
 
-				const float fU = fUNum / fDen;
-				const float fV = fVNum / fDen;
+				const float fr = __fdividef(1.0f, fDen);
+				const float fU = fUNum * fr;
+				const float fV = fVNum * fr;
 
-				fVal += tex3D(gT_coneProjTexture, fU, fV, fAngle);
+				fVal += tex3D(gT_coneProjTexture, fU, fV, fAngle) * fr;
 
 				fZs += fSubStep;
 			}
@@ -260,6 +241,119 @@ __global__ void dev_cone_BP_SS(void* D_volData, unsigned int volPitch, int start
 	}
 }
 
+struct Vec3 {
+	double x;
+	double y;
+	double z;
+	Vec3(double x_, double y_, double z_) : x(x_), y(y_), z(z_) { }
+	Vec3 operator+(const Vec3 &b) const {
+		return Vec3(x + b.x, y + b.y, z + b.z);
+	}
+	Vec3 operator-(const Vec3 &b) const {
+		return Vec3(x - b.x, y - b.y, z - b.z);
+	}
+	Vec3 operator-() const {
+		return Vec3(-x, -y, -z);
+	}
+	double norm() const {
+		return sqrt(x*x + y*y + z*z);
+	}
+};
+
+double det3x(const Vec3 &b, const Vec3 &c) {
+	return (b.y * c.z - b.z * c.y);
+}
+double det3y(const Vec3 &b, const Vec3 &c) {
+	return -(b.x * c.z - b.z * c.x);
+}
+
+double det3z(const Vec3 &b, const Vec3 &c) {
+	return (b.x * c.y - b.y * c.x);
+}
+
+double det3(const Vec3 &a, const Vec3 &b, const Vec3 &c) {
+	return a.x * det3x(b,c) + a.y * det3y(b,c) + a.z * det3z(b,c);
+}
+
+Vec3 cross3(const Vec3 &a, const Vec3 &b) {
+	return Vec3(det3x(a,b), det3y(a,b), det3z(a,b));
+}
+
+Vec3 scaled_cross3(const Vec3 &a, const Vec3 &b, const Vec3 &sc) {
+	Vec3 ret = cross3(a, b);
+	ret.x *= sc.y * sc.z;
+	ret.y *= sc.x * sc.z;
+	ret.z *= sc.x * sc.y;
+	return ret;
+}
+
+
+bool transferConstants(const SConeProjection* angles, unsigned int iProjAngles, const SProjectorParams3D& params)
+{
+	DevConeParams *p = new DevConeParams[iProjAngles];
+
+	// We need three things in the kernel:
+	// projected coordinates of pixels on the detector:
+
+	// u: || (x-s) v (s-d) || / || u v (s-x) ||
+	// v: -|| u (x-s) (s-d) || / || u v (s-x) ||
+
+	// ray density weighting factor for the adjoint
+	// || u v (s-d) ||^2 / ( |cross(u,v)| * || u v (s-x) ||^2 )
+
+	// FDK weighting factor
+	// ( || u v s || / || u v (s-x) || ) ^ 2
+
+
+
+	for (unsigned int i = 0; i < iProjAngles; ++i) {
+		Vec3 u(angles[i].fDetUX, angles[i].fDetUY, angles[i].fDetUZ);
+		Vec3 v(angles[i].fDetVX, angles[i].fDetVY, angles[i].fDetVZ);
+		Vec3 s(angles[i].fSrcX, angles[i].fSrcY, angles[i].fSrcZ);
+		Vec3 d(angles[i].fDetSX, angles[i].fDetSY, angles[i].fDetSZ);
+
+
+
+		double fScale;
+		if (!params.bFDKWeighting) {
+			// goal: 1/fDen^2 = || u v (s-d) ||^2 / ( |cross(u,v)| * || u v (s-x) ||^2 )
+			// fDen = ( sqrt(|cross(u,v)|) * || u v (s-x) || ) / || u v (s-d) || 
+			// i.e. scale = sqrt(|cross(u,v)|) * / || u v (s-d) ||
+
+
+			// NB: for cross(u,v) we invert the volume scaling (for the voxel
+			// size normalization) to get the proper dimensions for
+			// the scaling of the adjoint
+
+			fScale = sqrt(scaled_cross3(u,v,Vec3(params.fVolScaleX,params.fVolScaleY,params.fVolScaleZ)).norm()) / det3(u, v, s-d);
+		} else {
+			// goal: 1/fDen = || u v s || / || u v (s-x) ||
+			// fDen = || u v (s-x) || / || u v s ||
+			// i.e., scale = 1 / || u v s ||
+
+			fScale = 1.0 / det3(u, v, s);
+		}
+
+		p[i].fNumU.w = fScale * det3(s,v,d);
+		p[i].fNumU.x = fScale * det3x(v,s-d);
+		p[i].fNumU.y = fScale * det3y(v,s-d);
+		p[i].fNumU.z = fScale * det3z(v,s-d);
+		p[i].fNumV.w = -fScale * det3(s,u,d);
+		p[i].fNumV.x = -fScale * det3x(u,s-d);
+		p[i].fNumV.y = -fScale * det3y(u,s-d);
+		p[i].fNumV.z = -fScale * det3z(u,s-d);
+		p[i].fDen.w = fScale * det3(u, v, s); // == 1.0 for FDK
+		p[i].fDen.x = -fScale * det3x(u, v);
+		p[i].fDen.y = -fScale * det3y(u, v);
+		p[i].fDen.z = -fScale * det3z(u, v);
+	}
+
+	// TODO: Check for errors
+	cudaMemcpyToSymbol(gC_C, p, iProjAngles*sizeof(DevConeParams), 0, cudaMemcpyHostToDevice);
+
+	return true;
+}
+
 
 bool ConeBP_Array(cudaPitchedPtr D_volumeData,
                   cudaArray *D_projArray,
@@ -279,34 +373,9 @@ bool ConeBP_Array(cudaPitchedPtr D_volumeData,
 		if (th + angleCount > dims.iProjAngles)
 			angleCount = dims.iProjAngles - th;
 
-		// transfer angles to constant memory
-		float* tmp = new float[12*angleCount];
-
-
-		// NB: We increment angles at the end of the loop body.
-
-
-#define TRANSFER_TO_CONSTANT(expr,name) do { for (unsigned int i = 0; i < angleCount; ++i) tmp[12*i+name] = (expr) ; } while (0)
-
-		TRANSFER_TO_CONSTANT( (angles[i].fDetSZ - angles[i].fSrcZ)*angles[i].fDetVY - (angles[i].fDetSY - angles[i].fSrcY)*angles[i].fDetVZ , 0 );
-		TRANSFER_TO_CONSTANT( (angles[i].fDetSX - angles[i].fSrcX)*angles[i].fDetVZ -(angles[i].fDetSZ - angles[i].fSrcZ)*angles[i].fDetVX , 1 );
-		TRANSFER_TO_CONSTANT( (angles[i].fDetSY - angles[i].fSrcY)*angles[i].fDetVX - (angles[i].fDetSX - angles[i].fSrcX)*angles[i].fDetVY , 2 );
-		TRANSFER_TO_CONSTANT( (angles[i].fDetSY*angles[i].fDetVZ - angles[i].fDetSZ*angles[i].fDetVY)*angles[i].fSrcX - (angles[i].fDetSX*angles[i].fDetVZ - angles[i].fDetSZ*angles[i].fDetVX)*angles[i].fSrcY + (angles[i].fDetSX*angles[i].fDetVY - angles[i].fDetSY*angles[i].fDetVX)*angles[i].fSrcZ , 3 );
-
-		TRANSFER_TO_CONSTANT( (angles[i].fDetSY - angles[i].fSrcY)*angles[i].fDetUZ-(angles[i].fDetSZ - angles[i].fSrcZ)*angles[i].fDetUY, 4 );
-		TRANSFER_TO_CONSTANT( (angles[i].fDetSZ - angles[i].fSrcZ)*angles[i].fDetUX - (angles[i].fDetSX - angles[i].fSrcX)*angles[i].fDetUZ , 5 );
-		TRANSFER_TO_CONSTANT((angles[i].fDetSX - angles[i].fSrcX)*angles[i].fDetUY-(angles[i].fDetSY - angles[i].fSrcY)*angles[i].fDetUX , 6 );
-		TRANSFER_TO_CONSTANT( -(angles[i].fDetSY*angles[i].fDetUZ - angles[i].fDetSZ*angles[i].fDetUY)*angles[i].fSrcX + (angles[i].fDetSX*angles[i].fDetUZ - angles[i].fDetSZ*angles[i].fDetUX)*angles[i].fSrcY - (angles[i].fDetSX*angles[i].fDetUY - angles[i].fDetSY*angles[i].fDetUX)*angles[i].fSrcZ , 7 );
-
-		TRANSFER_TO_CONSTANT( angles[i].fDetUY*angles[i].fDetVZ - angles[i].fDetUZ*angles[i].fDetVY , 8 );
-		TRANSFER_TO_CONSTANT( angles[i].fDetUZ*angles[i].fDetVX - angles[i].fDetUX*angles[i].fDetVZ , 9 );
-		TRANSFER_TO_CONSTANT( angles[i].fDetUX*angles[i].fDetVY - angles[i].fDetUY*angles[i].fDetVX , 10 );
-		TRANSFER_TO_CONSTANT( -angles[i].fSrcX * (angles[i].fDetUY*angles[i].fDetVZ - angles[i].fDetUZ*angles[i].fDetVY) - angles[i].fSrcY * (angles[i].fDetUZ*angles[i].fDetVX - angles[i].fDetUX*angles[i].fDetVZ) - angles[i].fSrcZ * (angles[i].fDetUX*angles[i].fDetVY - angles[i].fDetUY*angles[i].fDetVX) , 11 );
-
-#undef TRANSFER_TO_CONSTANT
-		cudaMemcpyToSymbol(gC_C, tmp, angleCount*12*sizeof(float), 0, cudaMemcpyHostToDevice); 
-
-		delete[] tmp;
+		bool ok = transferConstants(angles, angleCount, params);
+		if (!ok)
+			return false;
 
 		dim3 dimBlock(g_volBlockX, g_volBlockY);
 
diff --git a/cuda/3d/fdk.cu b/cuda/3d/fdk.cu
index 1294721..92d3ef6 100644
--- a/cuda/3d/fdk.cu
+++ b/cuda/3d/fdk.cu
@@ -92,10 +92,9 @@ __global__ void devFDK_preweight(void* D_projData, unsigned int projPitch, unsig
 	// pi / (2 * iProjAngles)           : scaling of the integral over angles
 	// fVoxSize ^ 2                     : ...
 
-	const float fW1 = fSrcOrigin * fDetUSize * fDetVSize;
 	const float fW2 = fCentralRayLength / (fDetUSize * fSrcOrigin);
 	const float fW3 = fVoxSize * fVoxSize;
-	const float fW = fCentralRayLength * fW1 * fW1 * fW2 * fW3 * (M_PI / 2.0f) / (float)dims.iProjAngles;
+	const float fW = fCentralRayLength * fW2 * fW3 * (M_PI / 2.0f) / (float)dims.iProjAngles;
 
 	for (int detectorV = startDetectorV; detectorV < endDetectorV; ++detectorV)
 	{