Research on Teeth Positioning Based on Wavelet Transform and Edge Detection - Advances in Image and Graphics Technologies - page 290

 ∂ f ∂ f 

ˆ (, ) xy = arctan /

(11)

 

∂ x ∂ y

 

With these two equations, the amplitude and phase value of each pixel gradient can
be respectively calculated by the convolution of the template and image. Then the two
templates of G x and G y (respectively on behalf of the horizontal and vertical direction)
can be combined to constitute a gradient-based edge detection operator. For such
algorithms, there are differences among the scales and parameters of different tem-
plates, which could result in different functions. Among all the templates, Prewitt is
the most representative one. As shown in Figure 5, Prewitt operator is an ideal edge
template which can better detect the edge of an image.

1 0 -1 -1 -1 -1

1 0 -1 0 0 0

1 0 -1 1 1 1

Fig. 5. Prewitt Operator Template

The edge detection is often used to define the left and right boundaries of the teeth
position. In this article, Prewitt edge detection algorithm is adopted.

(a) Narrow Zone between Maxillary and Mandibular Teeth

(b) Edge Detection Result

Fig. 6. Edge Detection Result of Teeth Zone

The dividing line between the maxillary and mandibular teeth has been obtained
after the horizontal processing. Then center on the line and extend upward and
downward for respectively 250 and 150 lines, thus a narrow horizontal zone is ob-
tained. The edge detection result of this zone can be seen in Figure 6 ((a) is the nar-
row horizontal zone and (b) is its edge detection result).
As shown in Figure 6 (b), after the edge detection, there is more edge information
in the teeth zone. However, there is almost zero information in non-teeth zone.