diff --git a/python/core/geometry/qgsgeometry.sip b/python/core/geometry/qgsgeometry.sip
index 1c18e2b12677..759cd0ca5263 100644
--- a/python/core/geometry/qgsgeometry.sip
+++ b/python/core/geometry/qgsgeometry.sip
@@ -241,6 +241,47 @@ Returns true if WKB of the geometry is of WKBMulti* type
  :rtype: float
 %End
 
+    double hausdorffDistance( const QgsGeometry &geom ) const;
+%Docstring
+ Returns the Hausdorff distance between this geometry and ``geom``. This is basically a measure of how similar or dissimilar 2 geometries are.
+
+ This algorithm is an approximation to the standard Hausdorff distance. This approximation is exact or close enough for a large
+ subset of useful cases. Examples of these are:
+
+ - computing distance between Linestrings that are roughly parallel to each other,
+ and roughly equal in length. This occurs in matching linear networks.
+ - Testing similarity of geometries.
+
+ If the default approximate provided by this method is insufficient, use hausdorffDistanceDensify() instead.
+
+ In case of error -1 will be returned.
+
+.. versionadded:: 3.0
+.. seealso:: hausdorffDistanceDensify()
+ :rtype: float
+%End
+
+    double hausdorffDistanceDensify( const QgsGeometry &geom, double densifyFraction ) const;
+%Docstring
+ Returns the Hausdorff distance between this geometry and ``geom``. This is basically a measure of how similar or dissimilar 2 geometries are.
+
+ This function accepts a ``densifyFraction`` argument. The function performs a segment
+ densification before computing the discrete Hausdorff distance. The ``densifyFraction`` parameter
+ sets the fraction by which to densify each segment. Each segment will be split into a
+ number of equal-length subsegments, whose fraction of the total length is
+ closest to the given fraction.
+
+ This method can be used when the default approximation provided by hausdorffDistance()
+ is not sufficient. Decreasing the ``densifyFraction`` parameter will make the
+ distance returned approach the true Hausdorff distance for the geometries.
+
+ In case of error -1 will be returned.
+
+.. versionadded:: 3.0
+.. seealso:: hausdorffDistance()
+ :rtype: float
+%End
+
     QgsPointXY closestVertex( const QgsPointXY &point, int &atVertex /Out/, int &beforeVertex /Out/, int &afterVertex /Out/, double &sqrDist /Out/ ) const;
 %Docstring
  :rtype: QgsPointXY
diff --git a/src/core/geometry/qgsgeometry.cpp b/src/core/geometry/qgsgeometry.cpp
index 203d1ad68ed9..2a9b4f323a08 100644
--- a/src/core/geometry/qgsgeometry.cpp
+++ b/src/core/geometry/qgsgeometry.cpp
@@ -1447,6 +1447,28 @@ double QgsGeometry::distance( const QgsGeometry &geom ) const
   return g.distance( geom.d->geometry );
 }
 
+double QgsGeometry::hausdorffDistance( const QgsGeometry &geom ) const
+{
+  if ( !d->geometry || !geom.d->geometry )
+  {
+    return -1.0;
+  }
+
+  QgsGeos g( d->geometry );
+  return g.hausdorffDistance( geom.d->geometry );
+}
+
+double QgsGeometry::hausdorffDistanceDensify( const QgsGeometry &geom, double densifyFraction ) const
+{
+  if ( !d->geometry || !geom.d->geometry )
+  {
+    return -1.0;
+  }
+
+  QgsGeos g( d->geometry );
+  return g.hausdorffDistanceDensify( geom.d->geometry, densifyFraction );
+}
+
 QgsGeometry QgsGeometry::buffer( double distance, int segments ) const
 {
   if ( !d->geometry )
diff --git a/src/core/geometry/qgsgeometry.h b/src/core/geometry/qgsgeometry.h
index 30c433f544e5..76f2fce8315a 100644
--- a/src/core/geometry/qgsgeometry.h
+++ b/src/core/geometry/qgsgeometry.h
@@ -271,6 +271,45 @@ class CORE_EXPORT QgsGeometry
      */
     double distance( const QgsGeometry &geom ) const;
 
+    /**
+     * Returns the Hausdorff distance between this geometry and \a geom. This is basically a measure of how similar or dissimilar 2 geometries are.
+     *
+     * This algorithm is an approximation to the standard Hausdorff distance. This approximation is exact or close enough for a large
+     * subset of useful cases. Examples of these are:
+     *
+     * - computing distance between Linestrings that are roughly parallel to each other,
+     * and roughly equal in length. This occurs in matching linear networks.
+     * - Testing similarity of geometries.
+     *
+     * If the default approximate provided by this method is insufficient, use hausdorffDistanceDensify() instead.
+     *
+     * In case of error -1 will be returned.
+     *
+     * \since QGIS 3.0
+     * \see hausdorffDistanceDensify()
+     */
+    double hausdorffDistance( const QgsGeometry &geom ) const;
+
+    /**
+     * Returns the Hausdorff distance between this geometry and \a geom. This is basically a measure of how similar or dissimilar 2 geometries are.
+     *
+     * This function accepts a \a densifyFraction argument. The function performs a segment
+     * densification before computing the discrete Hausdorff distance. The \a densifyFraction parameter
+     * sets the fraction by which to densify each segment. Each segment will be split into a
+     * number of equal-length subsegments, whose fraction of the total length is
+     * closest to the given fraction.
+     *
+     * This method can be used when the default approximation provided by hausdorffDistance()
+     * is not sufficient. Decreasing the \a densifyFraction parameter will make the
+     * distance returned approach the true Hausdorff distance for the geometries.
+     *
+     * In case of error -1 will be returned.
+     *
+     * \since QGIS 3.0
+     * \see hausdorffDistance()
+     */
+    double hausdorffDistanceDensify( const QgsGeometry &geom, double densifyFraction ) const;
+
     /**
      * Returns the vertex closest to the given point, the corresponding vertex index, squared distance snap point / target point
      * and the indices of the vertices before and after the closest vertex.
diff --git a/src/core/geometry/qgsgeos.cpp b/src/core/geometry/qgsgeos.cpp
index b7f754d2d226..477ff4d24560 100644
--- a/src/core/geometry/qgsgeos.cpp
+++ b/src/core/geometry/qgsgeos.cpp
@@ -369,7 +369,7 @@ double QgsGeos::distance( const QgsAbstractGeometry *geom, QString *errorMsg ) c
     return distance;
   }
 
-  GEOSGeometry *otherGeosGeom = asGeos( geom, mPrecision );
+  GEOSGeomScopedPtr otherGeosGeom( asGeos( geom, mPrecision ) );
   if ( !otherGeosGeom )
   {
     return distance;
@@ -377,11 +377,55 @@ double QgsGeos::distance( const QgsAbstractGeometry *geom, QString *errorMsg ) c
 
   try
   {
-    GEOSDistance_r( geosinit.ctxt, mGeos, otherGeosGeom, &distance );
+    GEOSDistance_r( geosinit.ctxt, mGeos, otherGeosGeom.get(), &distance );
   }
   CATCH_GEOS_WITH_ERRMSG( -1.0 )
 
-  GEOSGeom_destroy_r( geosinit.ctxt, otherGeosGeom );
+  return distance;
+}
+
+double QgsGeos::hausdorffDistance( const QgsAbstractGeometry *geom, QString *errorMsg ) const
+{
+  double distance = -1.0;
+  if ( !mGeos )
+  {
+    return distance;
+  }
+
+  GEOSGeomScopedPtr otherGeosGeom( asGeos( geom, mPrecision ) );
+  if ( !otherGeosGeom )
+  {
+    return distance;
+  }
+
+  try
+  {
+    GEOSHausdorffDistance_r( geosinit.ctxt, mGeos, otherGeosGeom.get(), &distance );
+  }
+  CATCH_GEOS_WITH_ERRMSG( -1.0 )
+
+  return distance;
+}
+
+double QgsGeos::hausdorffDistanceDensify( const QgsAbstractGeometry *geom, double densifyFraction, QString *errorMsg ) const
+{
+  double distance = -1.0;
+  if ( !mGeos )
+  {
+    return distance;
+  }
+
+  GEOSGeomScopedPtr otherGeosGeom( asGeos( geom, mPrecision ) );
+  if ( !otherGeosGeom )
+  {
+    return distance;
+  }
+
+  try
+  {
+    GEOSHausdorffDistanceDensify_r( geosinit.ctxt, mGeos, otherGeosGeom.get(), densifyFraction, &distance );
+  }
+  CATCH_GEOS_WITH_ERRMSG( -1.0 )
 
   return distance;
 }
diff --git a/src/core/geometry/qgsgeos.h b/src/core/geometry/qgsgeos.h
index cf07861c02c5..e20346368f0e 100644
--- a/src/core/geometry/qgsgeos.h
+++ b/src/core/geometry/qgsgeos.h
@@ -84,6 +84,42 @@ class CORE_EXPORT QgsGeos: public QgsGeometryEngine
     QgsPoint *pointOnSurface( QString *errorMsg = nullptr ) const override;
     QgsAbstractGeometry *convexHull( QString *errorMsg = nullptr ) const override;
     double distance( const QgsAbstractGeometry *geom, QString *errorMsg = nullptr ) const override;
+
+    /**
+     * Returns the Hausdorff distance between this geometry and \a geom. This is basically a measure of how similar or dissimilar 2 geometries are.
+     *
+     * This algorithm is an approximation to the standard Hausdorff distance. This approximation is exact or close enough for a large
+     * subset of useful cases. Examples of these are:
+     *
+     * - computing distance between Linestrings that are roughly parallel to each other,
+     * and roughly equal in length. This occurs in matching linear networks.
+     * - Testing similarity of geometries.
+     *
+     * If the default approximate provided by this method is insufficient, use hausdorffDistanceDensify() instead.
+     *
+     * \since QGIS 3.0
+     * \see hausdorffDistanceDensify()
+     */
+    double hausdorffDistance( const QgsAbstractGeometry *geom, QString *errorMsg = nullptr ) const;
+
+    /**
+     * Returns the Hausdorff distance between this geometry and \a geom. This is basically a measure of how similar or dissimilar 2 geometries are.
+     *
+     * This function accepts a \a densifyFraction argument. The function performs a segment
+     * densification before computing the discrete Hausdorff distance. The \a densifyFraction parameter
+     * sets the fraction by which to densify each segment. Each segment will be split into a
+     * number of equal-length subsegments, whose fraction of the total length is
+     * closest to the given fraction.
+     *
+     * This method can be used when the default approximation provided by hausdorffDistance()
+     * is not sufficient. Decreasing the \a densifyFraction parameter will make the
+     * distance returned approach the true Hausdorff distance for the geometries.
+     *
+     * \since QGIS 3.0
+     * \see hausdorffDistance()
+     */
+    double hausdorffDistanceDensify( const QgsAbstractGeometry *geom, double densifyFraction, QString *errorMsg = nullptr ) const;
+
     bool intersects( const QgsAbstractGeometry *geom, QString *errorMsg = nullptr ) const override;
     bool touches( const QgsAbstractGeometry *geom, QString *errorMsg = nullptr ) const override;
     bool crosses( const QgsAbstractGeometry *geom, QString *errorMsg = nullptr ) const override;
diff --git a/tests/src/python/test_qgsgeometry.py b/tests/src/python/test_qgsgeometry.py
index 8a2a214c711d..ccaf8affc63c 100644
--- a/tests/src/python/test_qgsgeometry.py
+++ b/tests/src/python/test_qgsgeometry.py
@@ -4223,6 +4223,34 @@ def testClipped(self):
             self.assertTrue(compareWkt(result, exp, 0.00001),
                             "clipped: mismatch Expected:\n{}\nGot:\n{}\n".format(exp, result))
 
+    def testHausdorff(self):
+        tests = [["POLYGON((0 0, 0 2, 1 2, 2 2, 2 0, 0 0))", "POLYGON((0.5 0.5, 0.5 2.5, 1.5 2.5, 2.5 2.5, 2.5 0.5, 0.5 0.5))", 0.707106781186548],
+                 ["LINESTRING (0 0, 2 1)", "LINESTRING (0 0, 2 0)", 1],
+                 ["LINESTRING (0 0, 2 0)", "LINESTRING (0 1, 1 2, 2 1)", 2],
+                 ["LINESTRING (0 0, 2 0)", "MULTIPOINT (0 1, 1 0, 2 1)", 1],
+                 ["LINESTRING (130 0, 0 0, 0 150)", "LINESTRING (10 10, 10 150, 130 10)", 14.142135623730951]
+                 ]
+        for t in tests:
+            g1 = QgsGeometry.fromWkt(t[0])
+            g2 = QgsGeometry.fromWkt(t[1])
+            o = g1.hausdorffDistance(g2)
+            exp = t[2]
+            self.assertAlmostEqual(o, exp, 5,
+                                   "mismatch for {} to {}, expected:\n{}\nGot:\n{}\n".format(t[0], t[1], exp, o))
+
+    def testHausdorffDensify(self):
+        tests = [
+            ["LINESTRING (130 0, 0 0, 0 150)", "LINESTRING (10 10, 10 150, 130 10)", 0.5, 70.0]
+        ]
+        for t in tests:
+            g1 = QgsGeometry.fromWkt(t[0])
+            g2 = QgsGeometry.fromWkt(t[1])
+            densify = t[2]
+            o = g1.hausdorffDistanceDensify(g2, densify)
+            exp = t[3]
+            self.assertAlmostEqual(o, exp, 5,
+                                   "mismatch for {} to {}, expected:\n{}\nGot:\n{}\n".format(t[0], t[1], exp, o))
+
 
 if __name__ == '__main__':
     unittest.main()