ABSTRACT
We present a method for deriving a parametric description of a conic section (quadratic curve) in an image from the moments of the image with respect to several specially-constructed kernel functions. In contrast to Hough-transform-type methods, the moment approach requires no large accumulator array. Judicious implementation allows the parameters to be determined using five multiplication operations and six addition operations per pixel. The use of moments renders the calculation robust in the presence of high-frequency noise or texture and resistant to small-scale irregularities in the edge. Our method is generalizable to more complex classes of curves with more parameters as well as to surfaces in higher dimensions.
Subject(s)
Algorithms , Artificial Intelligence , Image Interpretation, Computer-Assisted/methods , Models, Theoretical , Pattern Recognition, Automated/methods , Computer SimulationABSTRACT
We present a general construction of functions whose moments serve to locate and parametrize step edges within an image. Previous use of moments to locate edges was limited to functions supported on a circular region, but our method allows the use of "custom-designed" functions supported on circles, rectangles, or any desired shape, and with graphs whose shape may be chosen with great freedom. We present analyses of the sensitivity of our method to pixelization errors or discrepancy between the image and an idealized edge model. The parametric edge description yielded by our method makes it especially suitable as a component of wedgelet image coding.
