Shape Recognition with the Flow Integration Transform

Abstract We present the Flow Integration Transform (FIT), a method for determining the presence of a preconceived shape in a gray-scale image. The expected shape serves as a filter for detecting potential targets. The FIT performs a line integral of the dot product of two vectors: (1) the “flow”, a vector equal to the gradient of the image's intensity but rotated counterclockwise by 90°, and (2) the local tangent to the path of integration. The path of integration follows the contour of the expected target. The integration is performed starting at each point in the image, producing a two-dimensional transform whose pixel value corresponds to the relative presence of the expected shape at each location in the input image. The transform exhibits the appealing feature that information widely dispersed in the image becomes concentrated in a local area of the transform. Compared to traditional template matching using two-dimensional convulution, the correlation in the FIT is inherently one-dimensional, resulting in less computation. Furthermore, by constraining operations to addition, subtraction, and shift-by-one-pixel, implementation in high-speed hardware is greatly facilitated, with total computation times in the microsecond range achievable with present hardware technology.