Blending fixes and test updates

Summary:
Changed `torch.cumprod` to `torch.prod` in blending functions and added more tests and benchmark tests.

This should fix the issue raised on GitHub.

Reviewed By: gkioxari

Differential Revision: D20163073

fbshipit-source-id: 4569fd37be11aa4435a3ce8736b55622c00ec718

Author: nikhilaravi

pytorch3d/renderer/blending.py

@@ -45,7 +45,7 @@ def sigmoid_alpha_blend(colors, fragments, blend_params) -> torch.Tensor:
     """
     Silhouette blending to return an RGBA image
       - **RGB** - choose color of the closest point.
-      - **A** - blend based on the 2D distance based probability map [0].
+      - **A** - blend based on the 2D distance based probability map [1].
 
     Args:
         colors: (N, H, W, K, 3) RGB color for each of the top K faces per pixel.
@@ -60,7 +60,7 @@ def sigmoid_alpha_blend(colors, fragments, blend_params) -> torch.Tensor:
     Returns:
         RGBA pixel_colors: (N, H, W, 4)
 
-    [0] Liu et al, 'Soft Rasterizer: A Differentiable Renderer for Image-based
+    [1] Liu et al, 'Soft Rasterizer: A Differentiable Renderer for Image-based
         3D Reasoning', ICCV 2019
     """
     N, H, W, K = fragments.pix_to_face.shape
@@ -73,20 +73,13 @@ def sigmoid_alpha_blend(colors, fragments, blend_params) -> torch.Tensor:
     # the face. Therefore use -1.0 *  fragments.dists to get the correct sign.
     prob = torch.sigmoid(-fragments.dists / blend_params.sigma) * mask
 
-    # The cumulative product ensures that alpha will be 1 if at least 1 face
-    # fully covers the pixel as for that face prob will be 1.0
-    # TODO: investigate why torch.cumprod backwards is very slow for large
-    # values of K.
-    # Temporarily replace this with exp(sum(log))) using the fact that
-    # a*b = exp(log(a*b)) = exp(log(a) + log(b))
-    # alpha = 1.0 - torch.cumprod((1.0 - prob), dim=-1)[..., -1]
-
-    alpha = 1.0 - torch.exp(torch.log((1.0 - prob)).sum(dim=-1))
-
+    # The cumulative product ensures that alpha will be 0.0 if at least 1
+    # face fully covers the pixel as for that face, prob will be 1.0.
+    # This results in a multiplication by 0.0 because of the (1.0 - prob)
+    # term. Therefore 1.0 - alpha will be 1.0.
+    alpha = torch.prod((1.0 - prob), dim=-1)
     pixel_colors[..., :3] = colors[..., 0, :]  # Hard assign for RGB
-    pixel_colors[..., 3] = alpha
-
-    pixel_colors = torch.clamp(pixel_colors, min=0, max=1.0)
+    pixel_colors[..., 3] = 1.0 - alpha
     return torch.flip(pixel_colors, [1])
 
 
@@ -95,7 +88,7 @@ def softmax_rgb_blend(
 ) -> torch.Tensor:
     """
     RGB and alpha channel blending to return an RGBA image based on the method
-    proposed in [0]
+    proposed in [1]
       - **RGB** - blend the colors based on the 2D distance based probability map and
         relative z distances.
       - **A** - blend based on the 2D distance based probability map.
@@ -151,15 +144,11 @@ def softmax_rgb_blend(
     # Sigmoid probability map based on the distance of the pixel to the face.
     prob_map = torch.sigmoid(-fragments.dists / blend_params.sigma) * mask
 
-    # The cumulative product ensures that alpha will be 1 if at least 1 face
-    # fully covers the pixel as for that face prob will be 1.0
-    # TODO: investigate why torch.cumprod backwards is very slow for large
-    # values of K.
-    # Temporarily replace this with exp(sum(log))) using the fact that
-    # a*b = exp(log(a*b)) = exp(log(a) + log(b))
-    # alpha = 1.0 - torch.cumprod((1.0 - prob), dim=-1)[..., -1]
-
-    alpha = 1.0 - torch.exp(torch.log((1.0 - prob_map)).sum(dim=-1))
+    # The cumulative product ensures that alpha will be 0.0 if at least 1
+    # face fully covers the pixel as for that face, prob will be 1.0.
+    # This results in a multiplication by 0.0 because of the (1.0 - prob)
+    # term. Therefore 1.0 - alpha will be 1.0.
+    alpha = torch.prod((1.0 - prob_map), dim=-1)
 
     # Weights for each face. Adjust the exponential by the max z to prevent
     # overflow. zbuf shape (N, H, W, K), find max over K.
@@ -178,8 +167,6 @@ def softmax_rgb_blend(
     weighted_colors = (weights[..., None] * colors).sum(dim=-2)
     weighted_background = (delta / denom) * background
     pix_colors[..., :3] = weighted_colors + weighted_background
-    pix_colors[..., 3] = alpha
+    pix_colors[..., 3] = 1.0 - alpha
 
-    # Clamp colors to the range 0-1 and flip y axis.
-    pix_colors = torch.clamp(pix_colors, min=0, max=1.0)
     return torch.flip(pix_colors, [1])

tests/bm_blending.py

@@ -0,0 +1,42 @@
+#!/usr/bin/env python3
+# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved
+
+
+from itertools import product
+from fvcore.common.benchmark import benchmark
+
+from test_blending import TestBlending
+
+
+def bm_blending() -> None:
+    devices = ["cpu", "cuda"]
+    kwargs_list = []
+    num_meshes = [16]
+    image_size = [128, 256]
+    faces_per_pixel = [50, 100]
+    test_cases = product(num_meshes, image_size, faces_per_pixel, devices)
+
+    for case in test_cases:
+        n, s, k, d = case
+        kwargs_list.append(
+            {
+                "num_meshes": n,
+                "image_size": s,
+                "faces_per_pixel": k,
+                "device": d,
+            }
+        )
+
+    benchmark(
+        TestBlending.bm_sigmoid_alpha_blending,
+        "SIGMOID_ALPHA_BLENDING_PYTORCH",
+        kwargs_list,
+        warmup_iters=1,
+    )
+
+    benchmark(
+        TestBlending.bm_softmax_blending,
+        "SOFTMAX_BLENDING_PYTORCH",
+        kwargs_list,
+        warmup_iters=1,
+    )