Stereo Ranging with verging Cameras Based on the paper by E. Krotkov, K.Henriksen and R. Kories

The system description Two cameras mounted on a platform can translate horizontally and vertically, and rotate left-right and up- down. Motors mounted on each lens adjust the focal length, focusing distance, and aperture diameter. Further, the two camera can verge by rotating towards each other (converging) or away form each other (diverging). The travel from minimum to maximum vergence angle is approximately 6degrees, covering 90,000motor steps. Potential advantage of vergence include increasing the field of view common to two cameras and constraining the stereo disparity.

Model The lens is modeled as pinhole. The lens centers are separated by a baseline distance b, and both lenses have focal length f. Each camera is associated with a reference frame L and R with origins at the lens center and Z axes coincident with the optic axes positive in the direction fo the scene. We define a Cyclopean reference frame W with origin at the midpoint of the baseline, Z-axes normal to the base line and X axis coincident with the baseline.

Vergence mechanism

Reference Frames

The problem

Computing Range

Perspective transformation yields the image coordinates

Derivation for Z

The distance

Relationship of parameters to observation

Indirect measurements

Getting f and baseline from measurements

Constrain on offset

Parameter identification

Parameter Identification Second, we acquire disparity data from the scene viewed with different vergence angles. We servo the vergence motor to N different positions. At each we digitize a stereo pair of images and identify conjugate image points for each of the M objects. The outcome of this procedure is MxN conjugate points below and the associate vergence motor positions V.

Parameter identification Third we search for the least square values for baseline and the offset.

Experimental Results

Figure explanation We identify conjugate image points for each of 7 objects. There were 9 vergence positions. For each vergence position 7 different distant places were measured. The outcome is 7 x 9 conjugate points and associated vergence motor ositions.

Distance versus disparity

Vergence Changes Baseline Distance

This figure illustrates the case when the center of rotation is not the same as the lens center