BLOB ANALYSIS

The objective of this step is to compute features, feature are properties of the image’s blobs

AREA

The area feature is defined as the sum of the points within that blob

$$A=\sum _{p\in R}1$$

BARYCENTRE

The barycentre is defined as the center of mass of the region

$$B=\left[\begin{array}{c}{i}_b\\ j_b\end{array}\right]:i_b=\frac{1}{A}\sum _{p\in R}i,j_b=\frac{1}{A}\sum _{p\in R}j$$

ORIENTATION

Orientation is defined as the angle $\theta$ between the horizontal axis and the major axis of the blob, defined as the axis of least moment of inertia (the axis perpendicular to the major axis is called minor axis)

ORIENTED BOUNDING BOX (MINIMUM ENCLOSING RECTANGLE)

The MER can be computed from the major and minor axis by finding the 4 points laying at the maximum distance from the barycenter and sliding the axis towards them

LENGTH AND WIDTH

Length is the extent of the object along the major axis and width the extent on the minor axis

$$L=d_{V_1{V}_2}=d_{V_3{V}_4}=\sqrt{(i_{V_1}-i_{V_2}{)}^2+(j_{V_1}-j_{V_2}{)}^2}$$ $$W=d_{V_1{V}_3}=d_{V_2{V}_4}=\sqrt{(i_{V_1}-i_{V_3}{)}^2+(j_{V_1}-j_{V_3}{)}^2}$$

RECTANGULARITY

$$R=\frac{A}{LW}$$

ELLIPTICITY

$$R=\frac{A}{A_{LW}}with{A}_{LW}=\frac{\pi }{4}LW$$

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