diff --git a/Modules/Compatibility/Deprecated/include/itkVectorResampleImageFilter.hxx b/Modules/Compatibility/Deprecated/include/itkVectorResampleImageFilter.hxx
index 5b03d599c38..f6c074f0b8f 100644
--- a/Modules/Compatibility/Deprecated/include/itkVectorResampleImageFilter.hxx
+++ b/Modules/Compatibility/Deprecated/include/itkVectorResampleImageFilter.hxx
@@ -114,7 +114,6 @@ VectorResampleImageFilter<TInputImage, TOutputImage, TInterpolatorPrecisionType>
   PointType inputPoint;  // Coordinates of current input pixel
 
   using ContinuousIndexType = ContinuousIndex<TInterpolatorPrecisionType, ImageDimension>;
-  ContinuousIndexType inputIndex;
 
   // Doc says this only works for VectorImage, but Image implementation says otherwise...
   const unsigned int numberOfComponents = this->GetInput()->GetNumberOfComponentsPerPixel();
@@ -131,7 +130,8 @@ VectorResampleImageFilter<TInputImage, TOutputImage, TInterpolatorPrecisionType>
 
     // Compute corresponding input pixel position
     inputPoint = m_Transform->TransformPoint(outputPoint);
-    inputPtr->TransformPhysicalPointToContinuousIndex(inputPoint, inputIndex);
+    const ContinuousIndexType inputIndex =
+      inputPtr->template TransformPhysicalPointToContinuousIndex<TInterpolatorPrecisionType>(inputPoint);
 
     // Evaluate input at right position and copy to the output
     if (m_Interpolator->IsInsideBuffer(inputIndex))
diff --git a/Modules/Core/ImageFunction/include/itkBSplineInterpolateImageFunction.h b/Modules/Core/ImageFunction/include/itkBSplineInterpolateImageFunction.h
index e4d6c6a18ee..f15f6b1908a 100644
--- a/Modules/Core/ImageFunction/include/itkBSplineInterpolateImageFunction.h
+++ b/Modules/Core/ImageFunction/include/itkBSplineInterpolateImageFunction.h
@@ -180,9 +180,9 @@ class ITK_TEMPLATE_EXPORT BSplineInterpolateImageFunction : public InterpolateIm
   CovariantVectorType
   EvaluateDerivative(const PointType & point) const
   {
-    ContinuousIndexType index;
+    const ContinuousIndexType index =
+      this->GetInputImage()->template TransformPhysicalPointToContinuousIndex<TCoordRep>(point);
 
-    this->GetInputImage()->TransformPhysicalPointToContinuousIndex(point, index);
     // No thread info passed in, so call method that doesn't need thread ID.
     return (this->EvaluateDerivativeAtContinuousIndex(index));
   }
@@ -222,9 +222,8 @@ class ITK_TEMPLATE_EXPORT BSplineInterpolateImageFunction : public InterpolateIm
   void
   EvaluateValueAndDerivative(const PointType & point, OutputType & value, CovariantVectorType & deriv) const
   {
-    ContinuousIndexType index;
-
-    this->GetInputImage()->TransformPhysicalPointToContinuousIndex(point, index);
+    const ContinuousIndexType index =
+      this->GetInputImage()->template TransformPhysicalPointToContinuousIndex<TCoordRep>(point);
 
     // No thread info passed in, so call method that doesn't need thread ID.
     this->EvaluateValueAndDerivativeAtContinuousIndex(index, value, deriv);
diff --git a/Modules/Core/ImageFunction/include/itkImageFunction.h b/Modules/Core/ImageFunction/include/itkImageFunction.h
index 09141df678d..a1ed4763aff 100644
--- a/Modules/Core/ImageFunction/include/itkImageFunction.h
+++ b/Modules/Core/ImageFunction/include/itkImageFunction.h
@@ -191,7 +191,7 @@ class ITK_TEMPLATE_EXPORT ImageFunction : public FunctionBase<Point<TCoordRep, T
   void
   ConvertPointToContinuousIndex(const PointType & point, ContinuousIndexType & cindex) const
   {
-    m_Image->TransformPhysicalPointToContinuousIndex(point, cindex);
+    cindex = m_Image->template TransformPhysicalPointToContinuousIndex<TCoordRep>(point);
   }
 
   /** Convert continuous index to nearest index. */
diff --git a/Modules/Nonunit/Review/test/itkDiscreteGaussianDerivativeImageFunctionTest.cxx b/Modules/Nonunit/Review/test/itkDiscreteGaussianDerivativeImageFunctionTest.cxx
index 1e019e05a19..001c8568486 100644
--- a/Modules/Nonunit/Review/test/itkDiscreteGaussianDerivativeImageFunctionTest.cxx
+++ b/Modules/Nonunit/Review/test/itkDiscreteGaussianDerivativeImageFunctionTest.cxx
@@ -138,9 +138,7 @@ itkDiscreteGaussianDerivativeImageFunctionTestND(int argc, char * argv[])
   out.GoToBegin();
 
   using PointType = typename GaussianDerivativeImageFunctionType::PointType;
-  PointType point;
-  using ContinuousIndexType = typename GaussianDerivativeImageFunctionType::ContinuousIndexType;
-  ContinuousIndexType cindex;
+  PointType           point;
   const unsigned long nop = inputImage->GetRequestedRegion().GetNumberOfPixels();
   unsigned long       pixelNumber = 0;
   while (!it.IsAtEnd())
@@ -157,8 +155,12 @@ itkDiscreteGaussianDerivativeImageFunctionTestND(int argc, char * argv[])
     }
     else
     {
+      using ContinuousIndexType = typename GaussianDerivativeImageFunctionType::ContinuousIndexType;
+      using ContinuousIndexValueType = typename ContinuousIndexType::ValueType;
+
       inputImage->TransformIndexToPhysicalPoint(it.GetIndex(), point);
-      inputImage->TransformPhysicalPointToContinuousIndex(point, cindex);
+      const ContinuousIndexType cindex =
+        inputImage->template TransformPhysicalPointToContinuousIndex<ContinuousIndexValueType>(point);
       out.Set(function->EvaluateAtContinuousIndex(cindex));
     }
     ++it;
diff --git a/Modules/Nonunit/Review/test/itkDiscreteGradientMagnitudeGaussianImageFunctionTest.cxx b/Modules/Nonunit/Review/test/itkDiscreteGradientMagnitudeGaussianImageFunctionTest.cxx
index faec402dd90..aa68bc58636 100644
--- a/Modules/Nonunit/Review/test/itkDiscreteGradientMagnitudeGaussianImageFunctionTest.cxx
+++ b/Modules/Nonunit/Review/test/itkDiscreteGradientMagnitudeGaussianImageFunctionTest.cxx
@@ -139,9 +139,7 @@ itkDiscreteGradientMagnitudeGaussianImageFunctionTestND(int argc, char * argv[])
   out.GoToBegin();
 
   using PointType = typename DiscreteGradientMagnitudeGaussianFunctionType::PointType;
-  PointType point;
-  using ContinuousIndexType = typename DiscreteGradientMagnitudeGaussianFunctionType::ContinuousIndexType;
-  ContinuousIndexType cindex;
+  PointType           point;
   const unsigned long nop = inputImage->GetRequestedRegion().GetNumberOfPixels();
   unsigned long       pixelNumber = 0;
   while (!it.IsAtEnd())
@@ -158,8 +156,12 @@ itkDiscreteGradientMagnitudeGaussianImageFunctionTestND(int argc, char * argv[])
     }
     else
     {
+      using ContinuousIndexType = typename DiscreteGradientMagnitudeGaussianFunctionType::ContinuousIndexType;
+      using ContinuousValueIndexType = typename ContinuousIndexType::ContinuousIndexType;
+
       inputImage->TransformIndexToPhysicalPoint(it.GetIndex(), point);
-      inputImage->TransformPhysicalPointToContinuousIndex(point, cindex);
+      const ContinuousIndexType cindex =
+        inputImage->TransformPhysicalPointToContinuousIndex<ContinuousValueIndexType>(point);
       out.Set(function->EvaluateAtContinuousIndex(cindex));
     }
     ++it;
diff --git a/Modules/Nonunit/Review/test/itkDiscreteHessianGaussianImageFunctionTest.cxx b/Modules/Nonunit/Review/test/itkDiscreteHessianGaussianImageFunctionTest.cxx
index 27dae98cea4..fe02807825b 100644
--- a/Modules/Nonunit/Review/test/itkDiscreteHessianGaussianImageFunctionTest.cxx
+++ b/Modules/Nonunit/Review/test/itkDiscreteHessianGaussianImageFunctionTest.cxx
@@ -132,9 +132,7 @@ itkDiscreteHessianGaussianImageFunctionTestND(int argc, char * argv[])
   IteratorType outIter(output, output->GetRequestedRegion());
 
   using PointType = typename HessianGaussianImageFunctionType::PointType;
-  PointType point;
-  using ContinuousIndexType = typename HessianGaussianImageFunctionType::ContinuousIndexType;
-  ContinuousIndexType cindex;
+  PointType           point;
   const unsigned long nop = reader->GetOutput()->GetRequestedRegion().GetNumberOfPixels();
   unsigned long       pixelNumber = 0;
   while (!it.IsAtEnd())
@@ -150,8 +148,12 @@ itkDiscreteHessianGaussianImageFunctionTestND(int argc, char * argv[])
     }
     else
     {
+      using ContinuousIndexType = typename HessianGaussianImageFunctionType::ContinuousIndexType;
+      using ContinuousIndexValueType = typename ContinuousIndexType::ValueType;
+
       reader->GetOutput()->TransformIndexToPhysicalPoint(it.GetIndex(), point);
-      reader->GetOutput()->TransformPhysicalPointToContinuousIndex(point, cindex);
+      const ContinuousIndexType cindex =
+        reader->GetOutput()->TransformPhysicalPointToContinuousIndex<ContinuousIndexValueType>(point);
       hessian = function->EvaluateAtContinuousIndex(cindex);
     }