## FSCI †

FSCI is the abbreviation of the Fuzzy Spline Curve Identifier developed by us.

Nowadays, with the spread of tablets and PDA devices which use pen input, direct sketch drawing on displays is rapidly becoming possible. Although recognition of handwriting has already been implemented, recognition of sketch drawing is still being researched. Therefore, we have given birth to a completely new method of recognizing sketch drawing of curves, called FSCI.

When we consider general drawing applications, basic shapes such as circle, ellipse, triangle, rectangle are needed. Therefore, past sketch recognition methods that can recognize "triangle", "rectangle" and such shapes to fit the use of drawing applications were popular . But in FSCI, to achieve general purposeness, we have intentionally excluded these shapes and limited the recognized objects to the 7 primitive geometrical curves (line, circle, circular arc, ellipse, elliptical arc, closed free curve, open free curve).

The reason behind this is that most of the complex CAD drawings can be presented as a combination of these 7 primitive curves. For an example, after recognizing the line from sketch drawing, it becomes very easy for the applications to identify shapes such as triangle or rectangle.

 Fig. 1 Basic curve shapes identified by FSCI

Identifying these 7 curve shapes seem to be simple at the first glance. But these contain inclusive relationships such as "circle is a special case of ellipse", "ellipse is a special case of closed free curve", "circle is a special case of circular arc", "ellipse is a special case of elliptical arc". Therefore, in the traditional methods which only make use of shape information, it is difficult to identify shapes that have inclusive relationships. In FSCI, we use a unique technique that uses the vagueness (also called fuzziness) of the drawing manner to understand the user's intentions in order to solve this problem.

 Fig. 2 The inclusive relationships of the curve shapes

Inside FSCI, the sketch drawing is represented as a fuzzy spline - which is a spline curve which contains fuzziness - by estimating the shape as well as the roughness of the drawing action.

Moreover, the identification is done by fuzzy reasoning that selects the most simple curve from among the possible curve shapes. As such, in FSCI, a sketch is identified as a simple curve when drawn roughly and on the other hand as a complex curve when drawn carefully. As a result, users can use these characteristics and convey their intentions to FSCI appropriately by controlling their drawing manner as well as the shape of drawing.

### Identifying characteristics of FSCI †

Fuzzy spline curve is an extension of the spline curve based on fuzzy sets so that it can represent the curve shape as well as the positional vagueness of sketch drawing. In FSCI, the fuzziness (vagueness) of each point of the sketched curve is calculated with proportion to the speed and the acceleration of the drawing manner and then the fuzzy spline is generated.

Fig. 3 shows few examples of input sketch curves.

 Fig. 3 Sketch curve

Fig. 4 shows fuzzy spline curves. The green circles shows the fuzziness at each point. Fuzziness becomes large in places drawn quickly, roughly and small in places drawn slowly, carefully.

 Fig. 4 Fuzzy spline curves

FSCI can distinguish curves by the difference of fuzziness in fuzzy splines. Here, when we focus on the 3 types of curves of Fig. 3, we can see that they are of almost same shape, although in Fig. 4 they have different fuzziness. This is because the curve in the left was drawn with rough and swift drawing manner, and the middle curve was drawn a little carefully, and the rightmost curve was drawn slowly and carefully. In other words, the drawing manner of these 3 curves are different and therefore considered to be drawn with different intentions. FSCI is a method that uses the difference of drawing manner to identify sketch drawings successfully.

The results of the fuzzy reasoning is the identified curve shown in red in Fig. 5. From the 3 curves, as the left curve has large fuzziness, the possibility of a circle has been detected. On the other hand, as the fuzziness is small in the right curve, the possibility of a simple curve isn't detected and as a result identified as a complex free curve. Like this, even though the shapes are similar, the three curves are distinguished as circle (C), ellipse (E) and closed free curve (FC).

 Fig. 5 Fuzzy spline curves and identified results

### Process of FSCI †

The process of FSCI consists of two steps which are fuzzy spline interpolation and geometrical primitive curve identification.

1. Fuzzy spline interpolation
1. Fuzziness generation process
1. Generate fuzziness of each point of the sketched curve according to the speed and acceleration of drawing.
2. Add the fuzziness to the sampled points and produce fuzzy point sequence
2. Fuzzy point interpolation process
1. By doing fuzzy spline interpolation on the fuzzy point sequence, the fuzzy spline is produced.
2. Geometrical curve identification process
1. Possibility evaluation process
1. Form the 3 hypothetical models called linear fuzzy model, circular fuzzy model, elliptic fuzzy model based on the fuzzy spline.
2. Fuzzy spline curve and hypothetical models are compared based on fuzzy measures and evaluated to produce 4 possibility values that are linearity, circularity, ellipticity and closedness.
2. Curve class estimation
1. Based on the extracted possibility values, fuzzy reasoning is done to select the most simplest possible curve primitive by using fuzzy neural network.
2. The primitive is decided based on the obtained grades of the 7 primitive curve classes.
3. The parameters that define the identified curve class are extracted from the hypothetical model or the fuzzy spline.