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c25fd83694
Summary: Small fixes to website rendering Reviewed By: jcjohnson Differential Revision: D23281746 fbshipit-source-id: c9dc8edd5e52f39d4e0e19f10ecc7e035b39feda
69 lines
4.7 KiB
Markdown
69 lines
4.7 KiB
Markdown
---
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hide_title: true
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sidebar_label: Cameras
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---
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# Cameras
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## Camera Coordinate Systems
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When working with 3D data, there are 4 coordinate systems users need to know
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* **World coordinate system**
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This is the system the object/scene lives - the world.
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* **Camera view coordinate system**
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This is the system that has its origin on the image plane and the `Z`-axis perpendicular to the image plane. In PyTorch3D, we assume that `+X` points left, and `+Y` points up and `+Z` points out from the image plane. The transformation from world to view happens after applying a rotation (`R`) and translation (`T`).
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* **NDC coordinate system**
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This is the normalized coordinate system that confines in a volume the renderered part of the object/scene. Also known as view volume. Under the PyTorch3D convention, `(+1, +1, znear)` is the top left near corner, and `(-1, -1, zfar)` is the bottom right far corner of the volume. The transformation from view to NDC happens after applying the camera projection matrix (`P`).
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* **Screen coordinate system**
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This is another representation of the view volume with the `XY` coordinates defined in pixel space instead of a normalized space.
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An illustration of the 4 coordinate systems is shown below
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## Defining Cameras in PyTorch3D
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Cameras in PyTorch3D transform an object/scene from world to NDC by first transforming the object/scene to view (via transforms `R` and `T`) and then projecting the 3D object/scene to NDC (via the projection matrix `P`, else known as camera matrix). Thus, the camera parameters in `P` are assumed to be in NDC space. If the user has camera parameters in screen space, which is a common use case, the parameters should transformed to NDC (see below for an example)
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We describe the camera types in PyTorch3D and the convention for the camera parameters provided at construction time.
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### Camera Types
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All cameras inherit from `CamerasBase` which is a base class for all cameras. PyTorch3D provides four different camera types. The `CamerasBase` defines methods that are common to all camera models:
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* `get_camera_center` that returns the optical center of the camera in world coordinates
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* `get_world_to_view_transform` which returns a 3D transform from world coordinates to the camera view coordinates (R, T)
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* `get_full_projection_transform` which composes the projection transform (P) with the world-to-view transform (R, T)
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* `transform_points` which takes a set of input points in world coordinates and projects to NDC coordinates ranging from [-1, -1, znear] to [+1, +1, zfar].
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* `transform_points_screen` which takes a set of input points in world coordinates and projects them to the screen coordinates ranging from [0, 0, znear] to [W-1, H-1, zfar]
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Users can easily customize their own cameras. For each new camera, users should implement the `get_projection_transform` routine that returns the mapping `P` from camera view coordinates to NDC coordinates.
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#### FoVPerspectiveCameras, FoVOrthographicCameras
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These two cameras follow the OpenGL convention for perspective and orthographic cameras respectively. The user provides the near `znear` and far `zfar` field which confines the view volume in the `Z` axis. The view volume in the `XY` plane is defined by field of view angle (`fov`) in the case of `FoVPerspectiveCameras` and by `min_x, min_y, max_x, max_y` in the case of `FoVOrthographicCameras`.
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#### PerspectiveCameras, OrthographicCameras
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These two cameras follow the Multi-View Geometry convention for cameras. The user provides the focal length (`fx`, `fy`) and the principal point (`px`, `py`). For example, `camera = PerspectiveCameras(focal_length=((fx, fy),), principal_point=((px, py),))`
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As mentioned above, the focal length and principal point are used to convert a point `(X, Y, Z)` from view coordinates to NDC coordinates, as follows
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```
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# for perspective
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x_ndc = fx * X / Z + px
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y_ndc = fy * Y / Z + py
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z_ndc = 1 / Z
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# for orthographic
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x_ndc = fx * X + px
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y_ndc = fy * Y + py
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z_ndc = Z
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```
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Commonly, users have access to the focal length (`fx_screen`, `fy_screen`) and the principal point (`px_screen`, `py_screen`) in screen space. In that case, to construct the camera the user needs to additionally provide the `image_size = ((image_width, image_height),)`. More precisely, `camera = PerspectiveCameras(focal_length=((fx_screen, fy_screen),), principal_point=((px_screen, py_screen),), image_size = ((image_width, image_height),))`. Internally, the camera parameters are converted from screen to NDC as follows:
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```
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fx = fx_screen * 2.0 / image_width
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fy = fy_screen * 2.0 / image_height
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px = - (px_screen - image_width / 2.0) * 2.0 / image_width
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py = - (py_screen - image_height / 2.0) * 2.0/ image_height
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```
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