Segmentation Edge-based

As with previous methods, an edge-based segmentation is applicable to a 2D image. For the segmentation of 3D volume data sets, the interactive generation of the target structure has to be applied to each slice of the volume. Note also that some techniques have been extended to operate in 3D (see Section 4.4.1, for example). 

Live-wire (Barret and Mortensen 1997), also called intelligent scissors (Mortensen and Barret 1995), is an edge-based segmentation technique based on the concept of intelligent contour genera-... 

Figure 2.27. Isothermal section at 307°C of the Al-Zn-Si diagram. The boundary binary systems are shown. The isothermal section at 307°C is marked on the binary Al-Zn diagram. The corresponding single-phase (thick segment) and two-phase regions are indicated in the base edge of the triangle. By additions of Si (immiscible in the solid state in the other two elements) two- and three-phase fields are formed. ( ) = three-phase region. In the two-phase region on the left examples of tie-lines are presented.

For a given point in the interior, draw the perpendicular line segments a, b, c to the three edges. Also, draw the (heavy) lines to the apices that divide the triangle into three smaller triangles ta, tb, tc, as shown. The formula for the area of a triangle (one-half the base times the height) allows us to write... 

The gradient-based segmentation, instead, allows to directly find the edges by their high-gradient magnitudes. 

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