I will not attempt to put down every math-laden detail of Zhang's routine, but I will cover the important points. Zhang takes in a model file and any number of image description files containing simply coordinates for all important points, each file having these coordinates in a certain (and the same) order. The coordinating sets of coordinates are all the image information that is necessary to calibrate a camera. Next Zhang transforms each set of points from a certain image to make them easier to work with; in his calculations, if points are left at large distances from the (very arbitrary) origin, some small differences in values are manipulated out of existence, and these small differences are the most important parts of the data.

   Now Zhang is ready to perform the calibration itself. First he estimates the transformations necessary to move from the 3-D coordinate system of the model that was photographed to the coordinate systems of each image taken; this can be done using the angles between points and some knowledge of perspective. Then he calls an optimizer (see my poster page for details), gives it all of the camera's internal parameters in matrix form, and evaluates the result of each step based on the 3-D distances between each point in the model file and its corresponding points in each image. The smaller the value of this function, the better the estimate of the camera parameters.

   Two methods of attempting to find a Plessey value for a miniscule-sized window (this is analogous to finding the instantaneous image derivative) are researched and explained: a gradient search and a scale-space search.

   The image gradient is a map of the derivatives of the image in all directions. The gradient corresponds very well to the error in detecting corner points by a modified Plessey algorithm (which actually finds the image derivatives in two directions); experiments have been conducted into the correspondence between each of the image gradient and the conjugate image gradient (perpendicular to the gradient) with the error in points found by the Plessey function. This error in calculated points is generally constant for a given set of images, implying that with a gradient with high enough contrast, the algorithm could have extremely close to zero maximum error.

   A scale-space search attempts to extrapolate the derivative values for an infinitessimally small area of the 2-D scene given the values of several windows of finite size. The larger the window, the less accurate the result, but at small enough pixel-size values--3 to 5 pixels across--the windows provide little information due to gradient blurring.

   A homogeneous coordinate system, adjusted for an unknown angle between the "plane" of the lens and the "plane" captured in the image, is used to model lens distortion. Heikkila and Silven use estimation of the camera view line, given an image, to help estimate camera coordinates with 1000% of normal previous accuracy.

   Contour-based detectors measure the contours, or curvatures, of the image function and select points of maximum or minimum curvature. They sometimes split curvatures into linear parts and locate intersections of large numbers of line segments.

   Intensity-based methods select points at the centers of multi-pixel-wide areas of high image gradient; in other words, they locate areas that stand out in color. One intensity-based method, known to Schmid as "Harris", uses the normals of a function known as the auto-correlatin matrix to determine interest points very simply: the larger the gradient in both directions at a point, the more likely it is to be of interest to us.

   Parametric intensity models fit parametric equations--I as a function of x and y-- to areas of the image to find areas of interest within the functions. They have very good accuracy, but can only operate in the two dimensions of the image, so they can basically only detect corners at very small angles with the conventional axes.