diff --git a/Modules/Core/Transform/include/itkKernelTransform.h b/Modules/Core/Transform/include/itkKernelTransform.h
index 22bacc413dc..24351ef78f2 100644
--- a/Modules/Core/Transform/include/itkKernelTransform.h
+++ b/Modules/Core/Transform/include/itkKernelTransform.h
@@ -225,6 +225,25 @@ class ITK_TEMPLATE_EXPORT KernelTransform : public Transform<TParametersValueTyp
     return Self::TransformCategoryEnum::Spline;
   }
 
+  /** Returns a boolean indicating whether it is possible or not to compute the
+   * inverse of this current Transform. If it is possible, then the inverse of
+   * the transform is returned in the inverseTransform variable passed by the
+   * user. Inverting is possible if the variable is not a null pointer.
+   */
+  bool
+  GetInverse(Self * inverseTransform) const;
+
+  using InverseTransformBasePointer = typename Superclass::InverseTransformBasePointer;
+
+  /** Return an inverse of this transform. */
+  InverseTransformBasePointer
+  GetInverseTransform() const override
+  {
+    Pointer inv = New();
+    this->GetInverse(inv);
+    return inv;
+  }
+
   /** Stiffness of the spline.  A stiffness of zero results in the
    * standard interpolating spline.  A non-zero stiffness allows the
    * spline to approximate rather than interpolate the landmarks.
diff --git a/Modules/Core/Transform/include/itkKernelTransform.hxx b/Modules/Core/Transform/include/itkKernelTransform.hxx
index bdd7057db44..f3662ef7bad 100644
--- a/Modules/Core/Transform/include/itkKernelTransform.hxx
+++ b/Modules/Core/Transform/include/itkKernelTransform.hxx
@@ -508,6 +508,43 @@ KernelTransform<TParametersValueType, VDimension>::GetFixedParameters() const ->
 }
 
 
+template <typename TParametersValueType, unsigned int VDimension>
+bool
+KernelTransform<TParametersValueType, VDimension>::GetInverse(Self * inverseTransform) const
+{
+  if (!inverseTransform)
+  {
+    return false;
+  }
+
+  auto deepCopyLandmarks = [](const typename PointSetType::ConstPointer source,
+                              typename PointSetType::Pointer            destination) {
+    typename PointSetType::PointsContainer::ConstIterator sourceIt = source->GetPoints()->Begin();
+
+    typename PointSetType::PointIdentifier i{ 0 };
+    while (sourceIt != source->GetPoints()->End())
+    {
+      destination->SetPoint(i, sourceIt->Value());
+      ++i;
+      ++sourceIt;
+    }
+  };
+
+  // make a deep copy of the source and target landmarks
+  typename PointSetType::Pointer sourceLandmarks = PointSetType::New();
+  typename PointSetType::Pointer targetLandmarks = PointSetType::New();
+  deepCopyLandmarks(this->GetSourceLandmarks(), sourceLandmarks);
+  deepCopyLandmarks(this->GetTargetLandmarks(), targetLandmarks);
+
+  // inversion comes from reversing the landmarks
+  inverseTransform->SetSourceLandmarks(targetLandmarks);
+  inverseTransform->SetTargetLandmarks(sourceLandmarks);
+  inverseTransform->SetStiffness(this->GetStiffness());
+  inverseTransform->ComputeWMatrix();
+
+  return true;
+}
+
 template <typename TParametersValueType, unsigned int VDimension>
 void
 KernelTransform<TParametersValueType, VDimension>::PrintSelf(std::ostream & os, Indent indent) const