diff --git a/src/aliceVision/fuseCut/DelaunayGraphCut.cpp b/src/aliceVision/fuseCut/DelaunayGraphCut.cpp
index b7454db77e..f309fe4673 100644
--- a/src/aliceVision/fuseCut/DelaunayGraphCut.cpp
+++ b/src/aliceVision/fuseCut/DelaunayGraphCut.cpp
@@ -1277,7 +1277,7 @@ DelaunayGraphCut::GeometryIntersection
 DelaunayGraphCut::intersectNextGeom(const DelaunayGraphCut::GeometryIntersection& inGeometry,
     const Point3d& originPt,
     const Point3d& dirVect, Point3d& intersectPt,
-    const float epsilon, const Point3d& lastIntersectPt) const
+    const double epsilonFactor, const Point3d& lastIntersectPt) const
 {
 
     switch (inGeometry.type)
@@ -1295,7 +1295,7 @@ DelaunayGraphCut::intersectNextGeom(const DelaunayGraphCut::GeometryIntersection
 
             const Facet intersectionFacet(tetrahedronIndex, i);
 
-            const GeometryIntersection result = rayIntersectTriangle(originPt, dirVect, intersectionFacet, intersectPt, epsilon, &lastIntersectPt);
+            const GeometryIntersection result = rayIntersectTriangle(originPt, dirVect, intersectionFacet, intersectPt, epsilonFactor, &lastIntersectPt);
             if (result.type != EGeometryType::None)
                 return result;
         }
@@ -1315,7 +1315,7 @@ DelaunayGraphCut::intersectNextGeom(const DelaunayGraphCut::GeometryIntersection
             // Define the facet to intersect
             const Facet facet(adjCellIndex, localVertexIndex);
 
-            const GeometryIntersection result = rayIntersectTriangle(originPt, dirVect, facet, intersectPt, epsilon, &lastIntersectPt);
+            const GeometryIntersection result = rayIntersectTriangle(originPt, dirVect, facet, intersectPt, epsilonFactor, &lastIntersectPt);
             if (result.type != EGeometryType::None)
                 return result;
         }
@@ -1339,7 +1339,7 @@ DelaunayGraphCut::intersectNextGeom(const DelaunayGraphCut::GeometryIntersection
 
             for (const Facet& facet : opositeFacets)
             {
-                const GeometryIntersection result = rayIntersectTriangle(originPt, dirVect, facet, intersectPt, epsilon, &lastIntersectPt);
+                const GeometryIntersection result = rayIntersectTriangle(originPt, dirVect, facet, intersectPt, epsilonFactor, &lastIntersectPt);
                 if (result.type != EGeometryType::None)
                     return result;
             }
@@ -1358,7 +1358,7 @@ DelaunayGraphCut::GeometryIntersection DelaunayGraphCut::rayIntersectTriangle(co
     const Point3d& DirVec,
     const DelaunayGraphCut::Facet& facet,
     Point3d& intersectPt,
-    const float epsilon, const Point3d* lastIntersectPt) const
+    const double epsilonFactor, const Point3d* lastIntersectPt) const
 {
     const VertexIndex AvertexIndex = getVertexIndex(facet, 0);
     const VertexIndex BvertexIndex = getVertexIndex(facet, 1);
@@ -1368,6 +1368,7 @@ DelaunayGraphCut::GeometryIntersection DelaunayGraphCut::rayIntersectTriangle(co
     const Point3d* B = &_verticesCoords[BvertexIndex];
     const Point3d* C = &_verticesCoords[CvertexIndex];
 
+    const double epsilon = std::min(std::min((*A - *B).size(), (*B - *C).size()), (*A - *C).size()) * epsilonFactor;
     Point3d tempIntersectPt;
     const Point2d triangleUv = getLineTriangleIntersectBarycCoords(&tempIntersectPt, A, B, C, &originPt, &DirVec);
 
diff --git a/src/aliceVision/fuseCut/DelaunayGraphCut.hpp b/src/aliceVision/fuseCut/DelaunayGraphCut.hpp
index 478e5c79be..af96720e60 100644
--- a/src/aliceVision/fuseCut/DelaunayGraphCut.hpp
+++ b/src/aliceVision/fuseCut/DelaunayGraphCut.hpp
@@ -378,12 +378,13 @@ class DelaunayGraphCut
      * @param originPt ray origin point
      * @param dirVect ray direction
      * @param intersectPt a reference that will store the computed intersection point for the intersected geometry
-     * @param epsilon used to define the boundary when we have to consider either a collision with an edge/vertex or a facet
+     * @param epsilonFactor a multiplicative factor on the smaller side of the facet  used to define the boundary when we
+     * have to consider either a collision with an edge/vertex or a facet.
      * @param lastIntersectPt constant reference to the last intersection point used to test the direction.
      * @return 
      */
     GeometryIntersection intersectNextGeom(const GeometryIntersection& inGeometry, const Point3d& originPt,
-        const Point3d& dirVect, Point3d& intersectPt, const float epsilon, const Point3d& lastIntersectPt) const;
+        const Point3d& dirVect, Point3d& intersectPt, const double epsilonFactor, const Point3d& lastIntersectPt) const;
 
     /**
      * @brief Function that returns the next geometry intersected by the ray on a given facet or None if there are no intersected geometry.
@@ -393,12 +394,13 @@ class DelaunayGraphCut
      * @param DirVec ray direction
      * @param facet the given facet to intersect with
      * @param intersectPt a reference that will store the computed intersection point for the next intersecting geometry
-     * @param epsilon used to define the boundary when we have to consider either a collision with an edge/vertex or a facet
+     * @param epsilonFactor a multiplicative factor on the smaller side of the facet  used to define the boundary when we
+     * have to consider either a collision with an edge/vertex or a facet.
      * @param lastIntersectPt pointer to the last intersection point used to test the direction (if not nulllptr)
      * @return 
      */
     GeometryIntersection rayIntersectTriangle(const Point3d& originPt, const Point3d& DirVec, const Facet& facet,
-        Point3d& intersectPt, const float epsilon, const Point3d* lastIntersectPt = nullptr) const;
+        Point3d& intersectPt, const double epsilonFactor, const Point3d* lastIntersectPt = nullptr) const;
 
     float distFcn(float maxDist, float dist, float distFcnHeight) const;