Energy for Segmentation

The energy for joint evaluation of segmentation and descriptor is given by the equation below.

equation 2: Energy for Segmentation

• u is STLD on 'R'

• v is STLD on 'R^c'

• a_i is the model of texture in 'R'

• a_o is model of texture on 'R^c'

The Energy is Similar to Mumford Shah energy with the key difference here that the descriptors are function of region 'R' and the standard convex techniques do not apply here. We use simple gradient decent to optimize this energy.

Equation 3: Gradient of Energy (equation 2)

Notice that in order to find the gradient we need to find the hat descriptor which is the solution of an extra PDE.

Equation 4: hat descriptor

Segmentation Evolution:

Segmentation Evolution achieved by STLD produce better results particularly near the boundaries,