Generation of test camera trajectories

Summary: Implements methods for generating trajectories of test cameras.

Reviewed By: nikhilaravi

Differential Revision: D26100869

fbshipit-source-id: cf2b61a34d4c749cd8cba881e97f6c388e57d1f8

projects/nerf/nerf/eval_video_utils.py

+# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
+import math
+from typing import Tuple
+
+import torch
+from pytorch3d.renderer import look_at_view_transform, PerspectiveCameras
+
+
+def generate_eval_video_cameras(
+    train_dataset,
+    n_eval_cams: int = 100,
+    trajectory_type: str = "figure_eight",
+    trajectory_scale: float = 0.2,
+    scene_center: Tuple[float, float, float] = (0.0, 0.0, 0.0),
+    up: Tuple[float, float, float] = (0.0, 0.0, 1.0),
+) -> dict:
+    """
+    Generate a camera trajectory for visualizing a NeRF model.
+
+    Args:
+        train_dataset: The training dataset object.
+        n_eval_cams: Number of cameras in the trajectory.
+        trajectory_type: The type of the camera trajectory. Can be one of:
+            circular: Rotating around the center of the scene at a fixed radius.
+            figure_eight: Figure-of-8 trajectory around the center of the
+                central camera of the training dataset.
+            trefoil_knot: Same as 'figure_eight', but the trajectory has a shape
+                of a trefoil knot (https://en.wikipedia.org/wiki/Trefoil_knot).
+            figure_eight_knot: Same as 'figure_eight', but the trajectory has a shape
+                of a figure-eight knot
+                (https://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)).
+        trajectory_scale: The extent of the trajectory.
+        up: The "up" vector of the scene (=the normal of the scene floor).
+            Active for the `trajectory_type="circular"`.
+        scene_center: The center of the scene in world coordinates which all
+            the cameras from the generated trajectory look at.
+    Returns:
+        Dictionary of camera instances which can be used as the test dataset
+    """
+    if trajectory_type in ("figure_eight", "trefoil_knot", "figure_eight_knot"):
+        cam_centers = torch.cat(
+            [e["camera"].get_camera_center() for e in train_dataset]
+        )
+        # get the nearest camera center to the mean of centers
+        mean_camera_idx = (
+            ((cam_centers - cam_centers.mean(dim=0)[None]) ** 2)
+            .sum(dim=1)
+            .min(dim=0)
+            .indices
+        )
+        # generate the knot trajectory in canonical coords
+        time = torch.linspace(0, 2 * math.pi, n_eval_cams + 1)[:n_eval_cams]
+        if trajectory_type == "trefoil_knot":
+            traj = _trefoil_knot(time)
+        elif trajectory_type == "figure_eight_knot":
+            traj = _figure_eight_knot(time)
+        elif trajectory_type == "figure_eight":
+            traj = _figure_eight(time)
+        traj[:, 2] -= traj[:, 2].max()
+
+        # transform the canonical knot to the coord frame of the mean camera
+        traj_trans = (
+            train_dataset[mean_camera_idx]["camera"]
+            .get_world_to_view_transform()
+            .inverse()
+        )
+        traj_trans = traj_trans.scale(cam_centers.std(dim=0).mean() * trajectory_scale)
+        traj = traj_trans.transform_points(traj)
+
+    elif trajectory_type == "circular":
+        cam_centers = torch.cat(
+            [e["camera"].get_camera_center() for e in train_dataset]
+        )
+
+        # fit plane to the camera centers
+        plane_mean = cam_centers.mean(dim=0)
+        cam_centers_c = cam_centers - plane_mean[None]
+
+        if up is not None:
+            # us the up vector instad of the plane through the camera centers
+            plane_normal = torch.FloatTensor(up)
+        else:
+            cov = (cam_centers_c.t() @ cam_centers_c) / cam_centers_c.shape[0]
+            _, e_vec = torch.symeig(cov, eigenvectors=True)
+            plane_normal = e_vec[:, 0]
+
+        plane_dist = (plane_normal[None] * cam_centers_c).sum(dim=-1)
+        cam_centers_on_plane = cam_centers_c - plane_dist[:, None] * plane_normal[None]
+
+        cov = (
+            cam_centers_on_plane.t() @ cam_centers_on_plane
+        ) / cam_centers_on_plane.shape[0]
+        _, e_vec = torch.symeig(cov, eigenvectors=True)
+        traj_radius = (cam_centers_on_plane ** 2).sum(dim=1).sqrt().mean()
+        angle = torch.linspace(0, 2.0 * math.pi, n_eval_cams)
+        traj = traj_radius * torch.stack(
+            (torch.zeros_like(angle), angle.cos(), angle.sin()), dim=-1
+        )
+        traj = traj @ e_vec.t() + plane_mean[None]
+
+    else:
+        raise ValueError(f"Uknown trajectory_type {trajectory_type}.")
+
+    # point all cameras towards the center of the scene
+    R, T = look_at_view_transform(
+        eye=traj,
+        at=(scene_center,),  # (1, 3)
+        up=(up,),  # (1, 3)
+        device=traj.device,
+    )
+
+    # get the average focal length and principal point
+    focal = torch.cat([e["camera"].focal_length for e in train_dataset]).mean(dim=0)
+    p0 = torch.cat([e["camera"].principal_point for e in train_dataset]).mean(dim=0)
+
+    # assemble the dataset
+    test_dataset = [
+        {
+            "image": None,
+            "camera": PerspectiveCameras(
+                focal_length=focal[None],
+                principal_point=p0[None],
+                R=R_[None],
+                T=T_[None],
+            ),
+            "camera_idx": i,
+        }
+        for i, (R_, T_) in enumerate(zip(R, T))
+    ]
+
+    return test_dataset
+
+
+def _figure_eight_knot(t: torch.Tensor, z_scale: float = 0.5):
+    x = (2 + (2 * t).cos()) * (3 * t).cos()
+    y = (2 + (2 * t).cos()) * (3 * t).sin()
+    z = (4 * t).sin() * z_scale
+    return torch.stack((x, y, z), dim=-1)
+
+
+def _trefoil_knot(t: torch.Tensor, z_scale: float = 0.5):
+    x = t.sin() + 2 * (2 * t).sin()
+    y = t.cos() - 2 * (2 * t).cos()
+    z = -(3 * t).sin() * z_scale
+    return torch.stack((x, y, z), dim=-1)
+
+
+def _figure_eight(t: torch.Tensor, z_scale: float = 0.5):
+    x = t.cos()
+    y = (2 * t).sin() / 2
+    z = t.sin() * z_scale
+    return torch.stack((x, y, z), dim=-1)