Method for determining optimal chamfer mask coefficients for distance transform

A method for determining optimal coefficients Ci,j, i being a row index varying from −P to +P and j a column index varying from −Q to +Q, P and Q being positive integers, of a distance transform chamfer mask providing estimations of distance between pixels of an image, said coefficients being approximations, to within a multiplicative scale factor n, n being a positive integer, of the distances of an image pixel subjected to the analysis of the chamfer mask with respect to the image pixels that are closest in the various so-called pixel directions of the mask, each coefficient being associated with the pixel of the mask whose distance it represents, and the determination consisting of a choice, for each coefficient, of a value selected from among a set of integer candidate values for the coefficient considered, said method comprising:

• a first sort operation among the integer candidate values for each coefficient with, as a first sort criteria, a maximum distance estimation error rate caused by the choice of a candidate value for a coefficient, in the estimations of distances of the image pixels aligned on an axis of displacement of the image corresponding to the direction going from an origin source pixel for the distance measurements that is subjected to the analysis of the chamfer mask to the pixel of the mask associated with the coefficient considered,
• a second sort operation among the integer candidate values issued from the first sort operation with, as second sort criteria, a maximum distance estimation error rate caused by the choice of two candidate values for a pair of coefficients, in the distance estimations of the image pixels contained in an angular sector of the image, delimited by two axes of displacement of the image corresponding to the directions going from the source pixel subjected to the analysis of the chamfer mask to the two pixels of the mask that are associated with the coefficients considered,
• an arbitrary selection operation of an integer candidate value issued from the first and second sorts for each coefficient whenever there is at least one integer candidate value issued from the first and second sort operations for each coefficient,
• an aborting operation of determining the optimal coefficients whenever there is not at least one integer candidate value issued from the first and second sort for each coefficient, and
• developing a two-dimensional map using the optimal coefficients.