Fair NURBS Curve Generation using a Hand-drawn Sketch for Computer Aided Aesthetic Design

Image processing techniques are used to detect the edges of a hand-drawn sketch. Generally, various types of gradation are expressed in the background of a hand-drawn sketch. Therefore, the original image is transformed into a logarithmic image. The entire image has to be binarized for edge detection. To smooth the edge of the binary image, feature based erosion and dilation is applied. A Laplacian operation is applied to the binary image to detect the edge in the binary image. This edge position corresponds to the position of the line in the hand-drawn sketch image. Line segments which represent the detected edges are generated. Using the positions and gradients on the line segments, a NURBS curve is generated. The shape of the NURBS curve extracted from the sketch image is examined by the designer visually. The shape of this NURBS curve generally coincides with the intention of the designer, but does not coincide precisely. Therefore, a curve shape modification method based on the specified radius of curvature is applied. The sum of the squared differences between the radius of curvature of a curve and the specified radius of curvature of an entire curve is linearized by Taylor’s theorem, then minimized. The specification of radius of curvature is performed by selecting a predefined fair NURBS curve using the similarity of radius of curvature distribution. Examples of NURBS curve generation based on a hand-drawn sketch are given according to the generation process. Key-Words: hand-drawn sketch, image processing, regression line, NURBS curve, curvature, radius of curvature, curve shape modification, correlation coefficient