Move sample_pdf into PyTorch3D

Summary: Copy the sample_pdf operation from the NeRF project in to PyTorch3D, in preparation for optimizing it.

Reviewed By: gkioxari

Differential Revision: D27117930

fbshipit-source-id: 20286b007f589a4c4d53ed818c4bc5f2abd22833

pytorch3d/renderer/implicit/sample_pdf.py

@@ -0,0 +1,83 @@
+# Copyright (c) Facebook, Inc. and its affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the BSD-style license found in the
+# LICENSE file in the root directory of this source tree.
+
+
+import torch
+
+
+def sample_pdf_python(
+    bins: torch.Tensor,
+    weights: torch.Tensor,
+    N_samples: int,
+    det: bool = False,
+    eps: float = 1e-5,
+) -> torch.Tensor:
+    """
+    Samples probability density functions defined by bin edges `bins` and
+    the non-negative per-bin probabilities `weights`.
+
+    Note: This is a direct conversion of the TensorFlow function from the original
+    release [1] to PyTorch.
+
+    Args:
+        bins: Tensor of shape `(..., n_bins+1)` denoting the edges of the sampling bins.
+        weights: Tensor of shape `(..., n_bins)` containing non-negative numbers
+            representing the probability of sampling the corresponding bin.
+        N_samples: The number of samples to draw from each set of bins.
+        det: If `False`, the sampling is random. `True` yields deterministic
+            uniformly-spaced sampling from the inverse cumulative density function.
+        eps: A constant preventing division by zero in case empty bins are present.
+
+    Returns:
+        samples: Tensor of shape `(..., N_samples)` containing `N_samples` samples
+            drawn from each probability distribution.
+
+    Refs:
+        [1] https://github.com/bmild/nerf/blob/55d8b00244d7b5178f4d003526ab6667683c9da9/run_nerf_helpers.py#L183  # noqa E501
+    """
+
+    # Get pdf
+    weights = weights + eps  # prevent nans
+    if weights.min() <= 0:
+        raise ValueError("Negative weights provided.")
+    pdf = weights / weights.sum(dim=-1, keepdim=True)
+    cdf = torch.cumsum(pdf, -1)
+    cdf = torch.cat([torch.zeros_like(cdf[..., :1]), cdf], -1)
+
+    # Take uniform samples u of shape (..., N_samples)
+    if det:
+        u = torch.linspace(0.0, 1.0, N_samples, device=cdf.device, dtype=cdf.dtype)
+        u = u.expand(list(cdf.shape[:-1]) + [N_samples]).contiguous()
+    else:
+        u = torch.rand(
+            list(cdf.shape[:-1]) + [N_samples], device=cdf.device, dtype=cdf.dtype
+        )
+
+    # Invert CDF
+    inds = torch.searchsorted(cdf, u, right=True)
+    # inds has shape (..., N_samples) identifying the bin of each sample.
+    below = (inds - 1).clamp(0)
+    above = inds.clamp(max=cdf.shape[-1] - 1)
+    # Below and above are of shape (..., N_samples), identifying the bin
+    # edges surrounding each sample.
+
+    inds_g = torch.stack([below, above], -1).view(
+        *below.shape[:-1], below.shape[-1] * 2
+    )
+    cdf_g = torch.gather(cdf, -1, inds_g).view(*below.shape, 2)
+    bins_g = torch.gather(bins, -1, inds_g).view(*below.shape, 2)
+    # cdf_g and bins_g are of shape (..., N_samples, 2) and identify
+    # the cdf and the index of the two bin edges surrounding each sample.
+
+    denom = cdf_g[..., 1] - cdf_g[..., 0]
+    denom = torch.where(denom < eps, torch.ones_like(denom), denom)
+    t = (u - cdf_g[..., 0]) / denom
+    # t is of shape  (..., N_samples) and identifies how far through
+    # each sample is in its bin.
+
+    samples = bins_g[..., 0] + t * (bins_g[..., 1] - bins_g[..., 0])
+
+    return samples