small fix for iou3d

Summary:
A small numerical fix for IoU for 3D boxes, fixes GH #992

* Adds a check for boxes with zero side areas (invalid boxes)
* Fixes numerical issue when two boxes have coplanar sides

Reviewed By: nikhilaravi

Differential Revision: D33195691

fbshipit-source-id: 8a34b4d1f1e5ec2edb6d54143930da44bdde0906

pytorch3d/csrc/iou_box3d/iou_box3d.cu

@@ -90,7 +90,8 @@ __global__ void IoUBox3DKernel(
         for (int b2 = 0; b2 < box2_count; ++b2) {
           const bool is_coplanar =
               IsCoplanarFace(box1_intersect[b1], box2_intersect[b2]);
-          if (is_coplanar) {
+          const float area = FaceArea(box1_intersect[b1]);
+          if ((is_coplanar) && (area > kEpsilon)) {
             tri2_keep[b2].keep = false;
           }
         }

pytorch3d/csrc/iou_box3d/iou_box3d_cpu.cpp

@@ -81,7 +81,8 @@ std::tuple<at::Tensor, at::Tensor> IoUBox3DCpu(
           for (int b2 = 0; b2 < box2_intersect.size(); ++b2) {
             const bool is_coplanar =
                 IsCoplanarFace(box1_intersect[b1], box2_intersect[b2]);
-            if (is_coplanar) {
+            const float area = FaceArea(box1_intersect[b1]);
+            if ((is_coplanar) && (area > kEpsilon)) {
               tri2_keep[b2] = 0;
             }
           }

pytorch3d/csrc/iou_box3d/iou_utils.cuh

@@ -138,6 +138,26 @@ FaceNormal(const float3 v0, const float3 v1, const float3 v2) {
   return n;
 }
 
+// The area of the face defined by vertices (v0, v1, v2)
+// Define e0 to be the edge connecting (v1, v0)
+// Define e1 to be the edge connecting (v2, v0)
+// Area is the norm of the cross product of e0, e1 divided by 2.0
+//
+// Args
+//    tri: FaceVerts of float3 coordinates of the vertices of the face
+//
+// Returns
+//    float: area for the face
+//
+__device__ inline float FaceArea(const FaceVerts& tri) {
+  // Get verts for face 1
+  const float3 v0 = tri.v0;
+  const float3 v1 = tri.v1;
+  const float3 v2 = tri.v2;
+  const float3 n = cross(v1 - v0, v2 - v0);
+  return norm(n) / 2.0;
+}
+
 // The normal of a box plane defined by the verts in `plane` with
 // the centroid of the box given by `center`.
 // Args

pytorch3d/csrc/iou_box3d/iou_utils.h

@@ -145,6 +145,26 @@ inline vec3<float> FaceNormal(vec3<float> v0, vec3<float> v1, vec3<float> v2) {
   return n;
 }
 
+// The area of the face defined by vertices (v0, v1, v2)
+// Define e0 to be the edge connecting (v1, v0)
+// Define e1 to be the edge connecting (v2, v0)
+// Area is the norm of the cross product of e0, e1 divided by 2.0
+//
+// Args
+//    tri: vec3 coordinates of the vertices of the face
+//
+// Returns
+//    float: area for the face
+//
+inline float FaceArea(const std::vector<vec3<float>>& tri) {
+  // Get verts for face
+  const vec3<float> v0 = tri[0];
+  const vec3<float> v1 = tri[1];
+  const vec3<float> v2 = tri[2];
+  const vec3<float> n = cross(v1 - v0, v2 - v0);
+  return norm(n) / 2.0;
+}
+
 // The normal of a box plane defined by the verts in `plane` with
 // the centroid of the box given by `center`.
 // Args

pytorch3d/ops/iou_box3d.py

@@ -69,6 +69,28 @@ def _check_coplanar(boxes: torch.Tensor, eps: float = 1e-4) -> None:
     return
 
 
+def _check_nonzero(boxes: torch.Tensor, eps: float = 1e-4) -> None:
+    """
+    Checks that the sides of the box have a non zero area
+    """
+    faces = torch.tensor(_box_triangles, dtype=torch.int64, device=boxes.device)
+    # pyre-fixme[16]: `boxes` has no attribute `index_select`.
+    verts = boxes.index_select(index=faces.view(-1), dim=1)
+    B = boxes.shape[0]
+    T, V = faces.shape
+    # (B, T, 3, 3) -> (B, T, 3)
+    v0, v1, v2 = verts.reshape(B, T, V, 3).unbind(2)
+
+    normals = torch.cross(v1 - v0, v2 - v0, dim=-1)  # (B, T, 3)
+    face_areas = normals.norm(dim=-1) / 2
+
+    if (face_areas < eps).any().item():
+        msg = "Planes have zero areas"
+        raise ValueError(msg)
+
+    return
+
+
 class _box3d_overlap(Function):
     """
     Torch autograd Function wrapper for box3d_overlap C++/CUDA implementations.
@@ -138,6 +160,8 @@ def box3d_overlap(
 
     _check_coplanar(boxes1, eps)
     _check_coplanar(boxes2, eps)
+    _check_nonzero(boxes1, eps)
+    _check_nonzero(boxes2, eps)
 
     # pyre-fixme[16]: `_box3d_overlap` has no attribute `apply`.
     vol, iou = _box3d_overlap.apply(boxes1, boxes2)

tests/test_iou_box3d.py

@@ -111,6 +111,11 @@ def _test_iou(self, overlap_fn, device):
         self.assertClose(
             vol, torch.tensor([[1 - dd]], device=vol.device, dtype=vol.dtype)
         )
+        # symmetry
+        vol, iou = overlap_fn(box2[None], box1[None])
+        self.assertClose(
+            vol, torch.tensor([[1 - dd]], device=vol.device, dtype=vol.dtype)
+        )
 
         # 3rd test
         dd = random.random()
@@ -119,6 +124,11 @@ def _test_iou(self, overlap_fn, device):
         self.assertClose(
             vol, torch.tensor([[1 - dd]], device=vol.device, dtype=vol.dtype)
         )
+        # symmetry
+        vol, _ = overlap_fn(box2[None], box1[None])
+        self.assertClose(
+            vol, torch.tensor([[1 - dd]], device=vol.device, dtype=vol.dtype)
+        )
 
         # 4th test
         ddx, ddy, ddz = random.random(), random.random(), random.random()
@@ -132,6 +142,16 @@ def _test_iou(self, overlap_fn, device):
                 dtype=vol.dtype,
             ),
         )
+        # symmetry
+        vol, _ = overlap_fn(box2[None], box1[None])
+        self.assertClose(
+            vol,
+            torch.tensor(
+                [[(1 - ddx) * (1 - ddy) * (1 - ddz)]],
+                device=vol.device,
+                dtype=vol.dtype,
+            ),
+        )
 
         # Also check IoU is 1 when computing overlap with the same shifted box
         vol, iou = overlap_fn(box2[None], box2[None])
@@ -152,6 +172,16 @@ def _test_iou(self, overlap_fn, device):
                 dtype=vol.dtype,
             ),
         )
+        # symmetry
+        vol, _ = overlap_fn(box2r[None], box1r[None])
+        self.assertClose(
+            vol,
+            torch.tensor(
+                [[(1 - ddx) * (1 - ddy) * (1 - ddz)]],
+                device=vol.device,
+                dtype=vol.dtype,
+            ),
+        )
 
         # 6th test
         ddx, ddy, ddz = random.random(), random.random(), random.random()
@@ -170,6 +200,17 @@ def _test_iou(self, overlap_fn, device):
             ),
             atol=1e-7,
         )
+        # symmetry
+        vol, _ = overlap_fn(box2r[None], box1r[None])
+        self.assertClose(
+            vol,
+            torch.tensor(
+                [[(1 - ddx) * (1 - ddy) * (1 - ddz)]],
+                device=vol.device,
+                dtype=vol.dtype,
+            ),
+            atol=1e-7,
+        )
 
         # 7th test: hand coded example and test with meshlab output
 
@@ -214,6 +255,10 @@ def _test_iou(self, overlap_fn, device):
         vol, iou = overlap_fn(box1r[None], box2r[None])
         self.assertClose(vol, torch.tensor([[vol_inters]], device=device), atol=1e-1)
         self.assertClose(iou, torch.tensor([[iou_mesh]], device=device), atol=1e-1)
+        # symmetry
+        vol, iou = overlap_fn(box2r[None], box1r[None])
+        self.assertClose(vol, torch.tensor([[vol_inters]], device=device), atol=1e-1)
+        self.assertClose(iou, torch.tensor([[iou_mesh]], device=device), atol=1e-1)
 
         # 8th test: compare with sampling
         # create box1
@@ -232,14 +277,20 @@ def _test_iou(self, overlap_fn, device):
         iou_sampling = self._box3d_overlap_sampling_batched(
             box1r[None], box2r[None], num_samples=10000
         )
-
+        self.assertClose(iou, iou_sampling, atol=1e-2)
+        # symmetry
+        vol, iou = overlap_fn(box2r[None], box1r[None])
         self.assertClose(iou, iou_sampling, atol=1e-2)
 
         # 9th test: non overlapping boxes, iou = 0.0
         box2 = box1 + torch.tensor([[0.0, 100.0, 0.0]], device=device)
         vol, iou = overlap_fn(box1[None], box2[None])
         self.assertClose(vol, torch.tensor([[0.0]], device=vol.device, dtype=vol.dtype))
         self.assertClose(iou, torch.tensor([[0.0]], device=vol.device, dtype=vol.dtype))
+        # symmetry
+        vol, iou = overlap_fn(box2[None], box1[None])
+        self.assertClose(vol, torch.tensor([[0.0]], device=vol.device, dtype=vol.dtype))
+        self.assertClose(iou, torch.tensor([[0.0]], device=vol.device, dtype=vol.dtype))
 
         # 10th test: Non coplanar verts in a plane
         box10 = box1 + torch.rand((8, 3), dtype=torch.float32, device=device)
@@ -284,6 +335,56 @@ def _test_iou(self, overlap_fn, device):
         vols, ious = overlap_fn(box_skew_1[None], box_skew_2[None])
         self.assertClose(vols, torch.tensor([[vol_inters]], device=device), atol=1e-1)
         self.assertClose(ious, torch.tensor([[iou]], device=device), atol=1e-1)
+        # symmetry
+        vols, ious = overlap_fn(box_skew_2[None], box_skew_1[None])
+        self.assertClose(vols, torch.tensor([[vol_inters]], device=device), atol=1e-1)
+        self.assertClose(ious, torch.tensor([[iou]], device=device), atol=1e-1)
+
+        # 12th test: Zero area bounding box (from GH issue #992)
+        box12a = torch.tensor(
+            [
+                [-1.0000, -1.0000, -0.5000],
+                [1.0000, -1.0000, -0.5000],
+                [1.0000, 1.0000, -0.5000],
+                [-1.0000, 1.0000, -0.5000],
+                [-1.0000, -1.0000, 0.5000],
+                [1.0000, -1.0000, 0.5000],
+                [1.0000, 1.0000, 0.5000],
+                [-1.0000, 1.0000, 0.5000],
+            ],
+            device=device,
+            dtype=torch.float32,
+        )
+
+        box12b = torch.tensor(
+            [
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+                [0.0, 0.0, 0.0],
+            ],
+            device=device,
+            dtype=torch.float32,
+        )
+        msg = "Planes have zero areas"
+        with self.assertRaisesRegex(ValueError, msg):
+            overlap_fn(box12a[None], box12b[None])
+        # symmetry
+        with self.assertRaisesRegex(ValueError, msg):
+            overlap_fn(box12b[None], box12a[None])
+
+        # 13th test: From GH issue #992
+        # Zero area coplanar face after intersection
+        ctrs = torch.tensor([[0.0, 0.0, 0.0], [-1.0, 1.0, 0.0]])
+        whl = torch.tensor([[2.0, 2.0, 2.0], [2.0, 2, 2]])
+        box13a = TestIoU3D.create_box(ctrs[0], whl[0])
+        box13b = TestIoU3D.create_box(ctrs[1], whl[1])
+        vol, iou = overlap_fn(box13a[None], box13b[None])
+        self.assertClose(vol, torch.tensor([[2.0]], device=vol.device, dtype=vol.dtype))
 
     def _test_real_boxes(self, overlap_fn, device):
         data_filename = "./real_boxes.pkl"
@@ -577,6 +678,13 @@ def box_planar_dir(box: torch.Tensor, eps=1e-4) -> torch.Tensor:
         msg = "Plane vertices are not coplanar"
         raise ValueError(msg)
 
+    # Check all faces have non zero area
+    area1 = torch.cross(v1 - v0, v2 - v0, dim=-1).norm(dim=-1) / 2
+    area2 = torch.cross(v3 - v0, v2 - v0, dim=-1).norm(dim=-1) / 2
+    if (area1 < eps).any().item() or (area2 < eps).any().item():
+        msg = "Planes have zero areas"
+        raise ValueError(msg)
+
     # We can write:  `ctr = v0 + a * e0 + b * e1 + c * n`, (1).
     # With <e0, n> = 0 and <e1, n> = 0, where <.,.> refers to the dot product,
     # since that e0 is orthogonal to n. Same for e1.
@@ -607,6 +715,27 @@ def box_planar_dir(box: torch.Tensor, eps=1e-4) -> torch.Tensor:
     return n
 
 
+def tri_verts_area(tri_verts: torch.Tensor) -> torch.Tensor:
+    """
+    Computes the area of the triangle faces in tri_verts
+    Args:
+        tri_verts: tensor of shape (T, 3, 3)
+    Returns:
+        areas: the area of the triangles (T, 1)
+    """
+    add_dim = False
+    if tri_verts.ndim == 2:
+        tri_verts = tri_verts.unsqueeze(0)
+        add_dim = True
+
+    v0, v1, v2 = tri_verts.unbind(1)
+    areas = torch.cross(v1 - v0, v2 - v0, dim=-1).norm(dim=-1) / 2.0
+
+    if add_dim:
+        areas = areas[0]
+    return areas
+
+
 def box_volume(box: torch.Tensor) -> torch.Tensor:
     """
     Computes the volume of each box in boxes.
@@ -988,7 +1117,10 @@ def box3d_overlap_naive(box1: torch.Tensor, box2: torch.Tensor):
     keep2 = torch.ones((tri_verts2.shape[0],), device=device, dtype=torch.bool)
     for i1 in range(tri_verts1.shape[0]):
         for i2 in range(tri_verts2.shape[0]):
-            if coplanar_tri_faces(tri_verts1[i1], tri_verts2[i2]):
+            if (
+                coplanar_tri_faces(tri_verts1[i1], tri_verts2[i2])
+                and tri_verts_area(tri_verts1[i1]) > 1e-4
+            ):
                 keep2[i2] = 0
     keep2 = keep2.nonzero()[:, 0]
     tri_verts2 = tri_verts2[keep2]