Coordinate Systems in 3D-PTV Algorithms


The 3D-PTV method aims to find the 3D positions of particles in flow by utilizing 2D images from different perspectives. This document discusses the coordinate systems involved in the 3D-PTV process.

Spatial Coordinates

There are two main spatial (3D) coordinate systems: Global Coordinates and Local Frame for each camera.

Global Coordinates: The base coordinate system, usually expressed in millimeters, is determined by the positions of points on a calibration target. The Z direction must be consistent with a right-handed system.

Local Frame: Each camera has its Local Frame, obtained from the Global Coordinates by rotation and translation. The origin is the camera’s primary point, and the Z axis points opposite the lens direction.

Image Coordinates

The relevant image coordinate systems include Pixel Coordinates, Metric Coordinates, and Flat Coordinates.

Pixel Coordinates: Row and column in the image data matrix, with the origin at the top-left of the image, y axis pointing down, x axis pointing right, and units in pixels.

Metric Coordinates: A linear transformation of Pixel Coordinates, with the origin at the image’s center point, y pointing up, x still pointing right, and units in millimeters.

Flat Coordinates: Derived from Metric Coordinates, considering lens distortion and sensor shift. Flat coordinates are obtained by adding sensor shift, calculating distorted coordinates, and correcting for distortion iteratively.


This document provides an overview of the coordinate systems used in 3D-PTV algorithms. For more details, refer to the comprehensive guide in ref. [1].

Image coordinate systems


[1] Draco, S. (2013). “Three-Dimensional Particle Tracking Velocimetry: A Review.”