Accurate measurement of curvilinear shapes by Virtual Image Correlation

Laboratoire FAST, Université Pierre et Marie Curie Paris 6, Université Paris-Sud 11, CNRS, Bat. 502, Campus Universitaire, 91405 Orsay, France

^a e-mail: marc.francois@univ-nantes.fr

Received: 11 July 2011
Accepted: 26 July 2011
Published online: 28 September 2011

Abstract

The proposed method allows the detection and the measurement, in the sense of metrology, of smooth elongated curvilinear shapes. Such measurements are required in many fields of physics, for example: mechanical engineering, biology or medicine (deflection of beams, fibers or filaments), fluid mechanics or chemistry (detection of fronts). Contrary to actual methods, the result is given in an analytical form of class C^∞ (and not a finite set of locations or pixels) thus curvatures and slopes, often of great interest in science, are given with good confidence. The proposed Virtual Image Correlation (VIC) method uses a virtual beam, an image which consists in a lateral expansion of the curve with a bell-shaped gray level. This figure is deformed until it fits the best the physical image with a method issued from the Digital Image Correlation method in use in solid mechanics. The precision of the identification is studied in a benchmark and successfully compared to two state-of-the-art methods. Three practical examples are given: a bar bending under its own weight, a thin fiber transported by a flow within a fracture and a thermal front. The first allows a comparison with theoretical solution, the second shows the ability of the method to deal with complex shapes and crossings and the third deals with ill-defined image.