Maximal directions discrepancy as accuracy criterion of images projective normalization for optical text recognition
The application of projective normalization (a special case of orthocorrection) to photographs of documents for their further optical recognition is generally accepted. To date, a number of criteria are known for the accuracy of projective normalization. Almost all of them characterize only the coordinates discrepancy. However, the text fields of documents usually have an elongated shape, so that even with small coordinates discrepancy, large directions discrepancy are possible, which significantly affect the quality of segmentation of the field and the recognition of individual characters in it. The problem of accurate correction of directions discrepancy also arises in tomography problems if a spiral scanning scheme is used for measurement or projections are recorded in tomosynthesis schemes. To describe images projective normalization accuracy at a point, a pointwise maximum directions discrepancy is proposed. As a criterion for projective normalization accuracy of the entire image, a maximum directions discrepancy equal to the maximum pointwise maximum directions discrepancy in the region of interest is proposed. An analytical solution to the problem of calculating the pointwise maximum directions discrepancy is obtained. A hypothesis was put forward and numerically confirmed that the pointwise maximum directions discrepancy is a quasiconvex function. The theorem is proved that the supremum of a quasiconvex function on a bounded closed set is equal to the supremum on the extreme points of its convex hull. Based on the hypothesis and theorem, an analytical solution to the problem of calculating the maximum directions discrepancy on the polyhedral region of interest is proposed.