PERF: Avoid processing entire rows based on mathematical certainties

When either the fixedMarginalPDF or movingMarginalPDF (which are sums of
rows or columns of the 2D joint histogram) then the intersection point
must also be zero.  Both the contribution to the final values of such a point
is no change, so one can avoid much testing and subsequent inner conditional
processing in such cases.

Modules/Registration/Metricsv4/include/itkMattesMutualInformationImageToImageMetricv4.hxx

@@ -365,9 +365,6 @@ MattesMutualInformationImageToImageMetricv4<TFixedImage,
   static constexpr PDFValueType closeToZero = std::numeric_limits<PDFValueType>::epsilon();
   const PDFValueType            nFactor = 1.0 / (this->m_MovingImageBinSize * this->GetNumberOfValidPoints());
 
-  // Setup pointer to point to the first bin
-  const JointPDFValueType * jointPDFPtr = l_JointPDF->GetBufferPointer();
-
   auto const temp_num_histogram_bins = this->m_NumberOfHistogramBins;
   /**
    * Compute the metric by double summation over histogram.
@@ -377,37 +374,36 @@ MattesMutualInformationImageToImageMetricv4<TFixedImage,
   {
     const PDFValueType fixedImageMarginalPDFValue = l_FixedImageMarginalPDF[fixedIndex];
 
-    const bool isNotNearZerofixedImageMarginalPDFValue = (fixedImageMarginalPDFValue > closeToZero);
-    // NOTE: if isNotNearZerofixedImageMarginalPDFValue is false, logfixedImageMarginalPDFValue is never used
-    //       The common case is that it is used, so only perform std::log(fixedImageMarginalPDFValue one time
-    const PDFValueType logfixedImageMarginalPDFValue = (isNotNearZerofixedImageMarginalPDFValue)
-                                                         ? std::log(fixedImageMarginalPDFValue)
-                                                         : std::numeric_limits<PDFValueType>::max();
+    // If fixedImageMarginalPDFValue is <= closeToZero, then the entire row of values is <= closeToZero, so
+    // by definition, each of the individual jointPDFVlaue's must also be close to zero in the line below!
+    if (fixedImageMarginalPDFValue > closeToZero)
     {
-      for (unsigned int movingIndex = 0; movingIndex < temp_num_histogram_bins;
-           ++movingIndex, ++jointPDFPtr /* GOTO NEXT BIN */)
+      // NOTE: If fixedImageMarginalPDFValue <=> closeToZero, logfixedImageMarginalPDFValue is never used
+      //       The common case is that it is used, so perform std::log(fixedImageMarginalPDFValue) one time
+      const PDFValueType logfixedImageMarginalPDFValue = std::log(fixedImageMarginalPDFValue);
+      // Setup pointer to point to the first bin of this row in the jointPDF
+      const JointPDFValueType * jointPDFRowPtr = l_JointPDF->GetBufferPointer() + fixedIndex * temp_num_histogram_bins;
+      for (unsigned int movingIndex = 0; movingIndex < temp_num_histogram_bins; ++movingIndex)
       {
         const PDFValueType & movingImageMarginalPDF = this->m_MovingImageMarginalPDF[movingIndex];
-        const PDFValueType & jointPDFValue = *(jointPDFPtr);
+        const PDFValueType   jointPDFValue = *(jointPDFRowPtr++); /* Get Value and goto next bin in row */
+
         // check for non-zero bin contribution, if movingImageMarginalPDF <= closeToZero, then so is joinPDFValue
-        if (movingImageMarginalPDF > closeToZero && jointPDFValue > closeToZero)
+        if (movingImageMarginalPDF > closeToZero &&
+            jointPDFValue > closeToZero) //<-- This check is always false if not isNotNearZerofixedImageMarginalPDFValue
         {
           const PDFValueType pRatio = std::log(jointPDFValue / movingImageMarginalPDF);
-          if (isNotNearZerofixedImageMarginalPDFValue)
-          {
-            sum += jointPDFValue * (pRatio - logfixedImageMarginalPDFValue);
-          }
+          sum += jointPDFValue * (pRatio - logfixedImageMarginalPDFValue);
 
           if (this->GetComputeDerivative())
           {
             if (!this->HasLocalSupport())
             {
               // Collect global derivative contributions
-
-              // move joint pdf derivative pointer to the right position
               JointPDFValueType const * derivPtr = this->m_JointPDFDerivatives->GetBufferPointer() +
                                                    (fixedIndex * this->m_JointPDFDerivatives->GetOffsetTable()[2]) +
                                                    (movingIndex * this->m_JointPDFDerivatives->GetOffsetTable()[1]);
+              // move joint pdf derivative pointer to the right position
               for (unsigned int parameter = 0, lastParameter = this->GetNumberOfLocalParameters();
                    parameter < lastParameter;
                    ++parameter, derivPtr++)