Active Region Growing

Recently the concept of active regions as a way to combine both region and boundary information has been introduced. Examples of this approach, called hybrid active regions, are the works of Paragios and Deriche [21], and Chakraborty et al. [22]. This model is a considerable extension on the active contour model since it incorporates region-based information with the aim of finding a partition where the interior and the exterior of the region preserve the desired image properties.

The goal of image segmentation is to partition the image into subregions with homogeneous properties in its interior and a high discontinuity with neighbouring regions in its boundary. With the aim of integrating both conditions, the global energy is defined with two basic terms. Boundary term measures the probability that boundary pixels are really edge pixels. Meanwhile, the region term measures the homogeneity in the interior of the regions by the probability that these pixels belong to each corresponding region. Some complementary definitions are required: let $\rho (R)=\{R_i:i\epsilon [0,N]\}$ be a partition of the image into $\{N+1\}$ non-overlapping regions, where $R_0$ is the region corresponding to the background region. Let $\partial \rho (R)=\{\partial R_i:i \epsilon [1,N]\}$ be the region boundaries of the partition $\rho (R)$. The energy function is then defined as

$$E(\rho (R)) = (1-\alpha) \sum_{i=1}^{N}-\log P_B(j:j\epsilo... ...) + \alpha \sum_{i=0}^{N}-\log P_R(j:j\epsilon R_i\vert R_i))$$ (3)

where $\alpha$ is a model parameter weighting both terms: boundary and region. This function is then optimised by a region competition algorithm [23] which takes the neighbouring pixels to the current region boundaries $\partial \rho (R)$ into account to determine the next movement. Specifically, a region aggregates a neighbouring pixel when this new classification decreases the energy of the segmentation. Intuitively, all regions begin to move and grow, competing for the pixels of the image until an energy minimum is reached. When the optimisation process finishes, if there is a background region $R_0$ which remains without being segmented, a new seed is placed in the core of the background and the energy minimisation starts again. This step allows a correct segmentation when a region was missed in the previous stage of initialisation. Furthermore, a final step merges adjacent regions if this causes the energy decrease.