Geometric and Radiometric Camera Calibration Shape From Stereo requires geometric knowledge of: –Cameras’ extrinsic parameters, i.e. the geometric relationship between the two cameras. –Camera intrinsic parameters, i.e. each camera’s internal geometry (e.g. Focal Length) and lens distortion effects. Shape From Shading requires radiometric knowledge of: –Camera detector uniformity (e.g. Flat-field images) –Camera detector temperature noise (e.g. Dark frame images) –Camera detector bad pixels –Camera Digital Number (DN) to radiance transfer function CSM4220 1

Camera Geometric Calibration This has been a computer vision research topic for many years (hence many papers) There are a number of available software tools to assist with the calibration process Examples include: –Matlab Camera Calibration ToolboxMatlab Camera Calibration Toolbox –Open CV Camera Calibration and 3D ReconstructionOpen CV Camera Calibration and 3D Reconstruction These often require a geometric calibration target – often a 2D checkerboard 2 CSM4220

Stereo Vision – calibration 3 A sequence of left and right camera images of a 16 × 16 square checker- board used as part of the intrinsic and extrinsic calibration procedure for the AU stereo WAC cameras. Left Camera Images Right Camera Images CSM4220

Stereo Vision – extrinsic calibration 4 Camera Baseline separation, and relative orientation CSM4220

Stereo Vision – intrinsic calibration 5 CSM4220

Stereo Vision – image rectification 6 CSM4220 Using the geometric calibration results, an image rectification algorithm is used to project two-or-more images onto a common image plane. It corrects image distortion by transforming the image into a standard coordinate system Image rectification illustrates how image rectification simplifies the search space in stereo correlation matching. (Image courtesy Bart van Andel) See Fusiello et al., A Compact algorithm for rectification of stereo pairs, Machine Vision Applications, 12, 16-22, 2000

7 Left rectified image Right rectified image ← ↓ Once rectified, a disparity algorithm searches along the rows to identify a pixel’s location in the right image relative to the left image. This pixel distance is often grey-scale coded (0 to 255) and shown as an image of the disparity map. Using epipolar geometry the 3D position of a pixel can be calculated (using triangulation). CSM4220 Stereo Vision – disparity maps

Stereo Vision – epipolar geometry and disparity 8 CSM4220 (Images courtesy Colorado School of Mines) b = camera baseline separation f = camera focal length V 1 and V 2 = horizontal placement of pixel points relative to camera centre (C) d = V 1 – V 2 = disparity D = Distance of point in real world y z x Eqn. derived from epipolar geometry above: D = b × f d

Stereo Vision – disparity map example 9 CSM4220 Zitnick-Kanade Stereo Algorithm Example: (See Experiments in Stereo Vision web page)Experiments in Stereo Vision Left imageRight imageGrey scaled disparity map Given camera geometry relative to the scene, then lighter pixels have greater disparity (nearer to cameras), whereas darker pixels have less disparity (further from cameras). D inversely proportional to d.

Stereo Vision – disparity to depth-maps 10 CSM4220 Grey scaled disparity map Using slide 8 eqn. the real-world x, y, z value for each pixel in the disparity map can be calculated relative to the camera origin. This can be regarded as an absolute depth-map. Just using the disparity map alone provides a relative depth-map. A mesh can be fitted to the 3D data points (compare laser scanner ‘point cloud’). Note errors due to disparity algorithm, and 8-bit grey-scale data. (GLView image above) 3D terrain models are referred to as height-maps, or Digital Elevation Models (DEM), or Digital Terrain Models (DTM).