This paper presents a multiscale shape representation approach for measuring the metrological characteristics of profiled fibers. From closed edge chains of a fiber cross section, three points are selected with evenly spaced indices to form a triangle, and the triangle area representation (TAR) is calculated with the determinant of a coordinate array of the three points. The bend direction of two consecutive lines drawn with the three vertices determines the sign of the TAR. Negative and positive TARs, denoted as TARN and TARP, respectively, are used to detect concave and convex segments on the boundary. The size of objects in a TARN or TARP graph reflects the degree of concaveness or convexness. If the index spacing is changed, a series of TARs with different scales can be obtained. Multiscale TARNs and TARPs can be used to recognize the basic shapes of profiled fibers, assess concavity, and detect fiber conglutinations for precise separation.
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