Projection Geometry
A linear mapping procedure projects a planar surface onto another plane by maintaining the perspective relationship between points on the two surfaces. A homography transform calculates the specific coordinates required to map a four-point quadrilateral from a captured image to a defined target orientation. Such calculations rely on the determination of a three by three matrix containing eight degrees of freedom that describe rotation, translation and scaling between the source and destination planes.
Machine vision systems utilize this mathematical operation to correct for sensor angle and lens distortion during the inspection of circuit board features.
Alignment Accuracy
Automated optical inspection equipment employs the method to normalize the perspective of a printed circuit board image before detecting component placement errors. Misalignment of the camera relative to the assembly surface creates trapezoidal distortion that shifts feature coordinates away from their true nominal values. Software applies a homography transform to reconstruct a top-down view that enables precise measurement of lead positions and solder fillet profiles.
Correcting these geometric variances prevents false rejections caused by perspective projection rather than genuine manufacturing defects.
Calibration Procedure
Engineers establish the reference points for this operation by measuring the distance between known markers on a calibration target during the initial setup of an assembly line station. Fixed dimensions on the physical artifact provide the ground truth for calculating the transformation matrix that maps incoming pixels to the physical coordinate system of the machine. The precision of the final inspection result depends entirely on the accuracy of these markers and the stability of the camera mount.
Small changes in distance between the lens and the board surface necessitate a complete update of the matrix to maintain the validity of subsequent automated tests.
