Coordinate Systems (Gemini)
A coordinate system is a mathematical framework that uses numbers (coordinates) to uniquely determine the position of points or geometric elements in space.
It relies on a fixed reference point, the origin, and reference lines or axes. Key types include Cartesian, polar, and geographic systems.
Common Usage Examples:
Cartesian Planes: Representing 2D points on a graph.
Geographical Mapping: Using latitude and longitude (spherical coordinates) to locate positions on Earth.
3D Modeling/Engineering: Using axes for modeling objects in space.
GPS Tracking: Determining precise locations on a map using spatial data.
There is no single mandatory coordinate system for all machine learning (ML) projects. The choice of coordinate system is dependent on the project's domain (e.g., 3D vision, GIS, robotics) and the data modality.
There are multiple, well-defined standards for specific tasks.
Here is a breakdown of the common systems and when to use them:
1. Computer Vision (2D/3D) Pixel/Image Coordinate System.
2. Geospatial/GIS Projects
Geographic Coordinate System (GCS): Uses 3D spherical surfaces (latitude and longitude).
3. Robotics & Industrial
Egocentric Coordinate System: Based on the robot's or camera's perspective ("left", "right", "front").
Absolute Coordinate System: Based on a fixed origin point in the environment.
Sensor Fusion (Lidar/Camera): Requires calibrating multiple sensors to a shared coordinate frame.
Key Takeaways
Consistency is Key: While not mandatory globally, the coordinate system must be consistent across all data used in a single training project (e.g., if one camera uses top-left origin, they all should).
Coordinate Transformation: Algorithms often need to transform coordinates (e.g., world to camera) using matrices.
Normalization: When feeding coordinates into a model, normalizing them to a consistent range (e.g., -1 to 1) is often preferred to keep numerical values stable.