Nonlinear Regression of Ink Spreading Using a General Ellipse Model

The behavior of ink spreading on hygroscopic media for printability was investigated using a high-speed camera and estimated using a rotated ellipse model. In the case of an ideal medium, an ink droplet spreads symmetrically and forms a circle. However, paper is a thin, heterogeneous and anisotropic material; thus, the speed of ink spreading differs according to the directions of the surface plane. Consequently, the ink spreading shapes a rotated ellipse rather than a circle; hence, a general ellipse was applied to build a model for the ink spreading. Boundary points of the ink spread are required to obtain the general ellipse model; hence, edge detectors were applied in consideration of the optical properties of the ink and medium. The edge detector was composed of area filters, thresholds, and Canny operation. The coefficients of the general ellipse model are obtained using a simplex search. The proposed method was tested using thin, heterogeneous and anisotropic media. The proposed method is useful for investigating the responses of ink paper and predicting the printability of ink-jetting.