Tools for handling pinhole camera parameters and plotting cameras.
# For development.
pip install -e .
# For install.
pip install .K : (3, 3) # Camera intrinsic matrix.
# [[fx, s, cx],
# [ 0, fy, cy],
# [ 0, 0, 1]]
# x: goes from top-left to top-right.
# y: goes from top-left to bottom-left.
R : (3, 3) # Rotation matrix.
Rc : (3, 3) # Rc = R.T = R.inv().
t : (3,) # Translation.
T : (4, 4) # Extrinsic matrix with (0, 0, 0, 1) row below.
# T = [R | t
# 0 | 1]
# T projects world space coordinate to the camera space
# (a.k.a view space or eye space). The camera center in world
# space projected by T becomes [0, 0, 0, 1]^T, i.e. the camera
# space has its origin at the camera center.
# T @ [[|], = [[0],
# [C], [0],
# [|], [0],
# [1]] [1]]
P : (3, 4) # World-to-pixel projection matrix. P = K @ [R | t] = K @ T[:3, :].
W2P : (4, 4) # World-to-pixel projection matrix. It is P with (0, 0, 0, 1)
# row below. When using W2P @ point_homo, the last
# element is always 1, thus it is ignored.
pose : (4, 4) # Camera pose. pose = T.inv(). pose[:3, :3] = R.T = Rc. pose[:3, 3] = C.
C : (3,) # Camera center.
Project 3D point [X, Y, Z, 1] to 2D [x, y, 1] pixel, e.g. with
pixels = ct.project.points_to_pixel(points, K, T).
# 0 -------> 1 (x)
# |
# |
# v (y)
cols = pixels[:, 0] # cols, width, x, top-left to top-right
rows = pixels[:, 1] # rows, height, y, top-left to bottom-left
cols = np.round(cols).astype(np.int32)
rows = np.round(rows).astype(np.int32)
cols[cols >= width] = width - 1
cols[cols < 0] = 0
rows[rows >= height] = height - 1
rows[rows < 0] = 0It can be confusing to use x, y, u, v. Prefer row and col.
# OpenGL convention:
# 1 (v)
# ^
# |
# |
# 0 -------> 1 (u)
# The following conversion accounts for pixel size
us = 1 / width * (0.5 + cols)
vs = 1 / height * (0.5 + (height - rows - 1))We choose to use 1D array for vector values like t and C. For example, t
is of shape (3, ) instead of (3, 1).
# The `@` operator can be directly used to dot a matrix and a vector
# - If both arguments are 2-D they are multiplied like conventional matrices.
# - If either argument is N-D, N > 2, it is treated as a stack of matrices
# residing in the last two indexes and broadcast accordingly.
# - If the first argument is 1-D, it is promoted to a matrix by prepending a 1
# to its dimensions. After matrix multiplication the prepended 1 is removed.
# - If the second argument is 1-D, it is promoted to a matrix by appending a 1
# to its dimensions. After matrix multiplication the appended 1 is removed.
# t is (3, ) and it is promoted to be (3, 1).
C = - R.T @ tpytest . -s
pytest camtools -s- Full unit tests
- PyTorch/Numpy wrapper (e.g. with
eagerpy)
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