Identification of QR Code Perspective Distortion Based on Edge Directions and Edge Projections Analysis

QR (quick response) Codes are one of the most popular types of two-dimensional (2D) matrix codes currently used in a wide variety of fields. Two-dimensional matrix codes, compared to 1D bar codes, can encode significantly more data in the same area. We have compared algorithms capable of localizing multiple QR Codes in an image using typical finder patterns, which are present in three corners of a QR Code. Finally, we present a novel approach to identify perspective distortion by analyzing the direction of horizontal and vertical edges and by maximizing the standard deviation of horizontal and vertical projections of these edges. This algorithm is computationally efficient, works well for low-resolution images, and is also suited to real-time processing.

Recognition of Car License Plates Using Morphological Information and SOM Algorithm

In this paper, we propose car license plate recognition using morphological information and a self-organizing map (SOM) algorithm. Morphological information on horizontal and vertical edges was used to extract the license plate from a car image. A 4-directional contour tracking algorithm was applied to extract the specific area, including characters, from an extracted plate. Recognition of extracted character strings was studied using the SOM algorithm. We used 50 car images to evaluate performance. Extraction for character strings by the proposed method showed better results than that from conventional color information on RGB and HSI. License plate recognition using the SOM algorithm was very efficient.

Pattern Avoidance in Permutations: Linear and Cyclic Orders

We generalize the notion of pattern avoidance to arbitrary functions on ordered sets, and consider specifically three scenarios for permutations: linear, cyclic and hybrid, the first one corresponding to classical permutation avoidance. The cyclic modification allows for circular shifts in the entries. Using two bijections, both ascribable to both Deutsch and Krattenthaler independently, we single out two geometrically significant classes of Dyck paths that correspond to two instances of simultaneous avoidance in the purely linear case, and to two distinct patterns in the hybrid case: non-decreasing Dyck paths (first considered by Barcucci et al.), and Dyck paths with at most one long vertical or horizontal edge. We derive a generating function counting Dyck paths by their number of low and high peaks, long horizontal and vertical edges, and what we call sinking steps. This translates into the joint distribution of fixed points, excedances, deficiencies, descents and inverse descents over 321-avoiding permutations. In particular we give an explicit formula for the number of 321-avoiding permutations with precisely $k$ descents, a problem recently brought up by Reifegerste. In both the hybrid and purely cyclic scenarios, we deal with the avoidance enumeration problem for all patterns of length up to 4. Simple Dyck paths also have a connection to the purely cyclic case; here the orbit-counting lemma gives a formula involving the Euler totient function and leads us to consider an interesting subgroup of the symmetric group.

Visual Sensitivity to the Shape and Size of a Moving Object: Implications for Models of Object Perception

Subjects adapted to rectangular targets whose opposite edges moved in opposite directions at any given instant (as when an object moves directly towards or away from the head). The distance that adaptation spread from the vertical edges was up to three times less when the horizontal edges were also moving than when the horizontal edges were stationary. Furthermore, for a square target (1 deg × 1 deg), adaptation spread least when the horizontal edges moved at the same speed as the vertical edges, whereas for a target whose height was half its width (0·5 deg × 1 deg) adaptation spread least when the horizontal edges moved at half the speed of the vertical edges. We propose that the human visual system acts as though it contains detectors sensitive to the size and shape of an object and that these detectors enhance this sensitivity to shape and size by comparing the velocities of the horizontal and vertical edges. When a nonrotating solid object moves in three dimensions its shape severely restricts the possible relationships between the velocities of the vertical and horizontal edges of its retinal image. Our hypothetical detectors utilise these geometrically determined velocity relationships as a basis for their selective sensitivity to shape. More speculatively, object perception and the perception of shape and size in everyday vision might involve visual sensitivity to the relationship between the velocities of an object's edges as well as sensitivity to the locations of these edges: the visual system may recognise which of the many edges in the visual field belong to a single object by comparing the velocities of orthogonal pairs of edges.