Terms and Definitions
Image is a mapping . Extremal regions are well defined on images if:
- is totally ordered (reflexive, antisymmetric and transitive binary relations exist).
- An adjacency relation is defined.
Region is a contiguous subset of . (For each there is a sequence and .
(Outer) Region Boundary, which means the boundary of is the set of pixels adjacent to at least one pixel of but not belonging to .
Extremal Region is a region such that either for all (maximum intensity region) or for all (minimum intensity region).
Maximally Stable Extremal Region Let be a sequence of nested extremal regions . Extremal region is maximally stable if and only if has a local minimum at . (Here denotes cardinality.) is a parameter of the method.
The equation checks for regions that remain stable over a certain number of thresholds. If a region is not significantly larger than a region, region is taken as a maximally stable region.
The concept more simply can be explained by thresholding. All the pixels below a given threshold are 'black' and all those above or equal are 'white'. If we are shown a sequence of thresholded images with frame corresponding to threshold t, we would see first a white image, then 'black' spots corresponding to local intensity minima will appear then grow larger. These 'black' spots will eventually merge, until the whole image is black. The set of all connected components in the sequence is the set of all extremal regions. In that sense, the concept of MSER is linked to the one of component tree of the image. The component tree indeed provide an easy way for implementing MSER.
Read more about this topic: Maximally Stable Extremal Regions
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