## Coordinate Systems in Lidar Toolbox

Lidar Toolbox™ uses these coordinate systems:

• Word — A fixed, universal coordinate system in which the physical sensors exist.

• Sensor — Specific to each particular sensor, such as a lidar sensor or a camera.

• Spatial — Specific to an image captured by a camera. Locations in spatial coordinates are expressed in pixels.

• Pattern — A checkerboard pattern coordinate system, typically used to calibrate camera sensors.

### World Coordinate System

The world coordinate system is a fixed universal system that works as an absolute reference for all sensors. Lidar Toolbox uses the right-handed Cartesian world coordinate system defined in ISO 8855, where the positive z-axis points up from the ground. Units are in meters.

### Sensor Coordinate System

A sensor coordinate system in Lidar Toolbox is anchored to a specific sensor, such as a lidar sensor or a camera. The location of each sensor contains the origin of its coordinate system. For example, the optical center of a camera typically acts as the origin of the camera coordinate system. Points in the sensor coordinate system follow these axes conventions:

• The x-axis points forward from the sensor.

• The y-axis points to the left, as viewed when facing forward.

• The z-axis points up from the ground to maintain the right-handed coordinate system.

The yaw, pitch, and roll angles of sensors follow an ISO convention. These angles are clockwise-positive when looking in the positive direction of the z-, y-, and x-axes, respectively.

### Spatial Coordinate System

Spatial coordinates enable you to specify a location in an image with greater granularity than pixel coordinates. In the pixel coordinate system, each pixel is treated as a discrete unit, uniquely identified by an integer row and column pair, such as (3,4). In the spatial coordinate system, locations in an image are represented in terms of partial pixels, such as (3.3,4.7).

### Pattern Coordinate System

A common technique for estimating the parameters of a monocular camera sensor is to calibrate the camera using multiple images of a calibration pattern, such as a checkerboard. In the pattern coordinate system, (XP, YP), the XP-axis points to the right and the YP-axis points down. The checkerboard origin is the bottom-right corner of the top-left square of the checkerboard.

Each checker corner represents one point in the coordinate system. For example, the corner to the right of the origin is (1,0) and the corner below the origin is (0,1). For more information on calibrating a camera by using a checkerboard pattern, see Calibrate a Monocular Camera (Automated Driving Toolbox).

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