Intrinsic and extrinsic calibrations

Camera calibration refers to both theintrinsic and extrinsic calibrations. The intrinsic calibration determines the optical properties of the camera lens,including the focal point (),principal point (),and distortion coefficients.

## What is geometric camera calibration?

What Is Camera Calibration? Geometric camera calibration, also referred to as camera resectioning, estimates the parameters of a lens and image sensor of an image or video camera. You can use these parameters to correct for lens distortion, measure the size of an object in world units, or determine the location of the camera in the scene.

## How are the camera parameters calculated during calibration?

In the process of calibration we calculate the camera parameters by a set of know 3D points and their corresponding pixel location in the image. For the 3D points we photograph a checkerboard pattern with known dimensions at many different orientations.

## How do I calibrate my camera?

Use the Camera Calibrator to perform camera calibration and evaluate the accuracy of the estimated parameters. The Computer Vision Toolbox? contains calibration algorithms for the pinhole camera model and the fisheye camera model. You can use the fisheye model with cameras up to a field of view (FOV) of 195 degrees.

## How does the calibration algorithm work?

The calibration algorithm calculates the camera matrix using the extrinsic and intrinsic parameters. The extrinsic parameters represent a rigid transformation from 3-D world coordinate system to the 3-D camera’s coordinate system.

## What Is Camera Calibration?

Geometric camera calibration, also referred to as** camera resectioning, estimates the parameters of a lens and image sensor of an image or video camera. ** You can use these parameters to correct for lens distortion, measure the size of an object in world units, or determine the location of the camera in the scene. These tasks are used in applications such as machine vision to detect and measure objects. They are also used in robotics, for navigation systems, and 3-D scene reconstruction.

## Why does the camera matrix not account for lens distortion?

The camera matrix does not account for lens distortion** because an ideal pinhole camera does not have a lens. ** To accurately represent a real camera, the camera model includes the radial and tangential lens distortion.

## What is the field of view of a fisheye camera?

You can use the fisheye model with cameras up to a field of view (FOV) of** 195 degrees. **

## What is a pinhole camera?

A pinhole camera is** a simple camera without a lens and with a single small aperture. ** Light rays pass through the aperture and project an inverted image on the opposite side of the camera. Think of the virtual image plane as being in front of the camera and containing the upright image of the scene.

## What is the calibration algorithm?

The calibration algorithm** calculates the camera matrix using the extrinsic and intrinsic parameters. ** The extrinsic parameters represent a rigid transformation from 3-D world coordinate system to the 3-D camera’s coordinate system. The intrinsic parameters represent a projective transformation from the 3-D camera’s coordinates into the 2-D image coordinates.

## What is the p1 and p2 of a lens?

p1 and p2 —** Tangential distortion coefficients of the lens. **

## What are the parameters of a camera?

Camera parameters include** intrinsics, extrinsics, and distortion coefficients. ** To estimate the camera parameters, you need to have 3-D world points and their corresponding 2-D image points. You can get these correspondences using multiple images of a calibration pattern, such as a checkerboard.

## What Is Camera Calibration?

Geometric camera calibration, also referred to as** camera resectioning, estimates the parameters of a lens and image sensor of an image or video camera. ** You can use these parameters to correct for lens distortion, measure the size of an object in world units, or determine the location of the camera in the scene. These tasks are used in applications such as machine vision to detect and measure objects. They are also used in robotics, for navigation systems, and 3-D scene reconstruction.

## What is radial distortion?

Radial distortion occurs** when light rays bend more near the edges of a lens than they do at its optical center. ** The smaller the lens, the greater the distortion.

## What are the extrinsic parameters of a camera?

The extrinsic parameters consist of a** rotation, R, and a translation, t. ** The origin of the camera’s coordinate system is at its optical center and its x- and y- axis define the image plane.

## What is the calibration algorithm?

The calibration algorithm calculates the camera matrix using the extrinsic and intrinsic parameters.** The extrinsic parameters represent a rigid transformation from 3-D world coordinate system to the 3-D camera’s coordinate system. The intrinsic parameters represent a projective transformation from the 3-D camera’s coordinates into the 2-D image coordinates. **

## What is a pinhole camera?

A pinhole camera is a simple camera without a lens and with a single** small aperture. ** Light rays pass through the aperture and project an inverted image on the opposite side of the camera. Think of the virtual image plane as being in front of the camera and containing the upright image of the scene.

## Why does the camera matrix not account for lens distortion?

The camera matrix does not account for lens distortion** because an ideal pinhole camera does not have a lens. ** To accurately represent a real camera, the camera model includes the radial and tangential lens distortion.

## What is camera calibration?

**The process of estimating the parameters of a camera ** is called camera calibration.

## What is the function that looks for a checkerboard and returns the coordinates of the corners?

**OpenCV ** provides a builtin function called findChessboardCorners that looks for a checkerboard and returns the coordinates of the corners. Let’ see the usage in the code block below. Its usage is given by

## What are the different types of camera calibration?

Following are the major types of camera calibration methods: 1 Calibration pattern: When we have complete control over the imaging process, the best way to perform calibration is to capture several images of an object or pattern of known dimensions from different view points. The checkerboard based method that we will learn in this post belongs to this category. We can also use circular patterns of known dimensions instead of checker board pattern. 2 Geometric clues: Sometimes we have other geometric clues in the scene like straight lines and vanishing points which can be used for calibration. 3 Deep Learning based: When we have very little control over the imaging setup (e.g. we have a single image of the scene), it may still be possible to obtain calibration information of the camera using a Deep Learning based method.

## Why are the corners of squares on a checkerboard important?

Not only that, the corners of squares on the checkerboard are ideal for localizing them because** they have sharp gradients in two directions. ** In addition, these corners are also related by the fact that they are at the intersection of checkerboard lines. All these facts are used to robustly locate the corners of the squares in a checkerboard pattern.

## What is the best way to perform calibration?

Calibration pattern: When we have complete control over the imaging process, the best way to perform calibration is** to capture several images of an object or pattern of known dimensions from different view points. ** The checkerboard based method that we will learn in this post belongs to this category. We can also use circular patterns of known dimensions instead of checker board pattern.

## What is the goal of the calibration process?

The goal of the calibration process is to** find the 3×3 matrix ** ,** the 3×3 rotation matrix ** ,** and the 3×1 translation vector using a set of known 3D points and their corresponding image coordinates ** . When we get the values of intrinsic and extrinsic parameters the camera is said to be calibrated.

## How to determine coordinates of 3D points?

Since points are equally spaced in the checkerboard, the** coordinates of each 3D point are easily defined by taking one point as reference (0, 0) and defining remaining with respect to that reference point. **

## Overview of Camera Calibration

A camera is a device that converts the 3D world into a 2D image. A camera plays a very important role in capturing three-dimensional images and storing them in two-dimensional images. To know the mathematics behind it is extremely fascinating. The following equation can represent the camera.

## What is camera calibration?

Camera calibration is the process of determining specific camera parameters in order to complete operations with specified performance measurements.

## A simple camera calibration method

In this section, we will look at a simple calibrating procedure. The important part is to get the right focal length because most of the parameters can be set using simple assumptions like square straight pixels, optical center at the middle of the image.

## Camera Model

Calibration techniques for the pinhole camera model and the fisheye camera model are included in the Computer Vision ToolboxTM. The fisheye variant is compatible with cameras with a field of vision (FOV) of up to 195 degrees.

## Types of distortion effects and their cause

We obtain better photos when we use a lens, yet the lens produces some distortion effects. Distortion effects are classified into two types:

## Mathematically representing lens distortion

When attempting to estimate the 3D points of the real world from an image, we must account for distortion effects.

## Removing distortion

So what do we do after the calibration step? We got the camera matrix and distortion coefficients in the previous post on camera calibration but how do we use the values?