Sekai Dataset Camera Conventions & Extrinsics Explained

Hey there! It's awesome you're diving into the Sekai dataset. We're thrilled you're finding it useful! Let's clear up those questions about the camera annotations. Understanding the coordinate system and how the extrinsics are handled is crucial for getting the most out of the data, and we're happy to provide the details.

Understanding the Camera Coordinate Convention in Sekai

When working with 3D data, the camera coordinate convention is one of the first things you need to nail down. It defines how points in the real world are mapped into the camera's view. In the Sekai dataset, we've adopted a standard convention that's widely used in computer vision and robotics to ensure compatibility and ease of use with existing tools and libraries. Our camera coordinate system is right-handed, meaning if you point your right thumb along the X-axis, your index finger along the Y-axis, and your middle finger along the Z-axis, they will be mutually perpendicular. The +X axis typically points to the right from the camera's perspective, the +Y axis points downwards from the camera's perspective, and the +Z axis points forward, directly out of the camera's lens. This convention is particularly useful because it aligns with how many image processing libraries and rendering engines represent pixel coordinates (where the origin is often the top-left corner, X increases to the right, and Y increases downwards). So, when you're transforming points from world coordinates into camera coordinates, remember that a positive Z value means the point is in front of the camera. This forward-looking Z-axis is a common choice for simplifying projection and depth calculations. We chose this specific convention to align with common practices in the field, making it easier for you to integrate Sekai data into your existing pipelines or to compare results with other research. It's important to note that while some systems use a left-handed coordinate system or have the camera looking along the -Z axis, our implementation sticks to the right-handed, +Z forward convention. This clarity in convention is vital for accurate 3D reconstructions, pose estimations, and any application that relies on precise spatial understanding of the scene captured by the cameras. We've found this to be a robust choice that minimizes confusion and maximizes interoperability with popular frameworks like OpenCV and PyTorch3D, which often assume similar conventions. So, to recap, in Sekai, think of the camera's view as: X to the right, Y down, and Z forward. This setup should feel intuitive if you've worked with camera models before, and if you're new to it, it's a solid convention to learn as it's quite prevalent.

What Does "Normalized" Mean for Extrinsics?

Now, let's talk about "normalized" extrinsics. This term, as mentioned in the README, refers to a specific transformation applied to the extrinsic camera parameters, which define the camera's pose (position and orientation) in the 3D world. In Sekai, we normalize the extrinsics to bring them into a canonical frame that simplifies transformations and ensures consistency across different camera setups or scenes. Essentially, normalization here means that the extrinsic matrix (often represented as a 4x4 transformation matrix $T_{cw}$) is adjusted such that the camera's origin (its position in the world) is effectively centered or scaled in a standard way, and its orientation is represented relative to a common world coordinate system. This process typically involves decomposing the extrinsic matrix into rotation and translation components and then applying a global scaling or centering operation. For instance, if your raw extrinsic matrices represent cameras at vastly different distances or in differently scaled environments, normalization helps to bring them to a comparable scale. It's not about simply scaling the translation vector; it's a more comprehensive transformation that might involve unifying the scale of the scene or ensuring the camera's reference point is consistently positioned relative to the origin of the world coordinate system. This can be particularly useful for algorithms that are sensitive to the absolute scale of the scene or that assume a specific bounding box or reference space for the cameras. By normalizing, we aim to remove variations that are due to the arbitrary placement and scaling of the coordinate system in which the original poses were defined. This ensures that when you use the extrinsic parameters, you are focusing on the relative poses of the cameras and objects within a standardized environment, rather than being influenced by the absolute scale or position of the camera rig itself. Think of it as putting all the cameras into a common, standardized stage where their relative positions and orientations are the focus, free from the distractions of varying absolute world scales. This makes it easier to compare results, train models that are less sensitive to scene scale, and perform tasks like multi-view geometry that benefit from consistent spatial references. The precise method of normalization can vary, but in our case, it's designed to establish a consistent spatial reference frame for all camera poses. This is crucial for tasks that require accurate measurements or comparisons across different views, as it prevents the absolute scale of the world or the camera's position from dominating the interpretation of the pose information. We ensure that the relative transformations between cameras and the scene are preserved accurately while abstracting away arbitrary world-scale factors.

Practical Implications and Usage

Understanding these conventions is key for using the Sekai dataset effectively. When you're performing transformations, such as projecting 3D points onto the 2D image plane or transforming points from one camera's coordinate system to another, always keep these conventions in mind. For projection, you'll typically use the camera's intrinsic matrix (focal length, principal point) along with the extrinsic matrix to map world points to pixel coordinates. Remember that the Z-axis in our camera convention points forward, which is important for depth calculations and understanding what's visible. The normalized extrinsics simplify the initial setup, ensuring that your transformations start from a consistent baseline. If you're comparing results from different experiments or using libraries that have their own default conventions, you might need to adjust your matrices accordingly. For example, if a library expects a left-handed system or a camera looking along -Z, you'll need to perform a coordinate transformation. We recommend checking the documentation of the specific tools you're using and comparing their conventions to ours. Often, a simple matrix multiplication or swapping of axes can resolve differences. The normalization of extrinsics means you can generally trust the relative pose information without worrying too much about the absolute scale of the scene in which the data was captured. This is particularly beneficial for training deep learning models that learn spatial relationships, as it allows the model to focus on the geometry rather than being confused by varying scene sizes. If you ever need to revert to or understand the original, unnormalized extrinsics (though we generally advise against it for most standard tasks), you would need information about the specific normalization process applied, which involves the inverse transformation. However, for most applications like 3D reconstruction, pose estimation, or scene understanding, working with the provided normalized extrinsics will yield the best and most consistent results. We've put effort into making these parameters as user-friendly as possible, reducing the common friction points when working with camera data. Always refer back to this explanation if you encounter unexpected behavior in your 3D vision tasks. It's the small details like coordinate conventions and normalization that often make the difference between a project that works smoothly and one that's a constant struggle.

Example Code Snippet (Conceptual)

To give you a more concrete idea, here's a conceptual Python-like snippet illustrating how you might use these parameters. Note that actual implementation details will depend on your chosen libraries (e.g., NumPy, PyTorch, OpenCV).

import numpy as np

# Assume you have your camera intrinsic matrix 'K'
# K is a 3x3 matrix containing focal length and principal point
# Example:
K = np.array([
    [fx, 0, cx],
    [0, fy, cy],
    [0, 0, 1]
])

# Assume you have your normalized extrinsic matrix 'T_cw'
# T_cw is a 4x4 matrix representing [R | t]
# R is the 3x3 rotation matrix from camera to world
# t is the 3x1 translation vector from camera origin to world origin
# In Sekai, this is already normalized for consistency.
# Example (conceptual):
T_cw = np.array([
    [r11, r12, r13, tx],
    [r21, r22, r23, ty],
    [r31, r32, r33, tz],
    [0, 0, 0, 1]
])

# To get the extrinsic matrix from world to camera (T_wc):
# This is often what's needed for projecting points
T_wc = np.linalg.inv(T_cw)

# Separate Rotation (R_wc) and Translation (t_wc) from T_wc
R_wc = T_wc[:3, :3]
t_wc = T_wc[:3, 3]

# Let's say you have a 3D point in world coordinates 'P_world'
P_world = np.array([x_w, y_w, z_w, 1]) # Homogeneous coordinates

# Project P_world onto the camera image plane:
# 1. Transform world point to camera coordinates:
P_camera = T_cw @ P_world # Using T_cw for consistency

# Note: Our convention is +Z forward, +X right, +Y down
# If you used T_wc and got P_camera = [Xc, Yc, Zc, 1], Zc is depth

# 2. Project into normalized image coordinates (if needed, often skipped)
# P_normalized_image = np.array([Xc/Zc, Yc/Zc])

# 3. Transform to pixel coordinates using the intrinsic matrix K:
# P_pixel_homogeneous = K @ np.array([Xc, Yc, Zc])
# P_pixel = P_pixel_homogeneous[:2] / P_pixel_homogeneous[2]

# For instance, if P_camera = [Xc, Yc, Zc, 1]:
# Depth is Zc
depth = P_camera[2]

# Pixel coordinates (u, v)
# This is the standard projection pipeline:
# [u, v, 1]^T = K @ [X_c/Z_c, Y_c/Z_c, 1]^T
# Or equivalently: [u, v, w]^T = K @ [X_c, Y_c, Z_c]^T, then u=u/w, v=v/w

u = (K[0, 0] * P_camera[0] / depth) + K[0, 2]
v = (K[1, 1] * P_camera[1] / depth) + K[1, 2]

print(f"3D World Point: {P_world[:3]}")
print(f"Transformed to Camera Coordinates (using T_cw): {P_camera[:3]}")
print(f"Depth: {depth}")
print(f"Projected Pixel Coordinates (u, v): ({u:.2f}, {v:.2f})")

# Important: Always ensure your point representations (e.g., 3D points)
# and matrices are using compatible dimensions (e.g., homogeneous coordinates).
# The exact matrix multiplication order and axis interpretation can vary based on
# the specific library and its underlying conventions.

We hope this detailed explanation clarifies the camera conventions and the meaning of normalized extrinsics in the Sekai dataset. If you have any more questions as you work with the data, please don't hesitate to ask!

For further reading on camera models and transformations, you might find resources from ** OpenCV Documentation and ** PyTorch3D documentation helpful, as they often discuss these concepts in detail.