Maximally stable extremal regions


In computer vision, maximally stable extremal regions are used as a method of blob detection in images. This technique was proposed by :cs:Jiří_Matas|Matas et al. to find correspondences between image elements from two images with different viewpoints. This method of extracting a comprehensive number of corresponding image elements contributes to the wide-baseline matching, and it has led to better stereo matching and object recognition algorithms.

Terms and definitions

Image is a mapping. Extremal regions are well defined on images if:
  1. is totally ordered.
  2. An adjacency relation is defined.
Region is a contiguous subset of. Note that under this definition the region can contain "holes".
region boundary, which means the boundary of is the set of pixels adjacent to at least one pixel of but not belonging to. Again, in case of regions with "holes", the region boundary is not obliged to be connected subset of .
Extremal region is a region such that either for all or for all . As far as is totally ordered, we can reformulate these conditions as for maximum intensity region and for minimum intensity region, respectively. In this form we can use a notion of a threshold intensity value which separates the region and its boundary.
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. is a parameter of the method. In practice, the subscript is not just a sequential index; means "region thresholded by intensity value ", which implies and.
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'. Given a source image, if a sequence of thresholded result images is generated where each image corresponds to an increasing threshold t, first a white image would be seen, 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.

Extremal regions

Extremal regions in this context have two important properties, that the set is closed under...
  1. continuous transformation of image coordinates. This means it is affine invariant and it doesn't matter if the image is warped or skewed.
  2. monotonic transformation of image intensities. The approach is of course sensitive to natural lighting effects as change of day light or moving shadows.

    Advantages of MSER

Because the regions are defined exclusively by the intensity function in the region and the outer border, this leads to many key characteristics of the regions which make them useful. Over a large range of thresholds, the local binarization is stable in certain regions, and have the properties listed below.
Note, however, that detection of MSERs in a scale pyramid improves repeatability, and number of correspondences across scale changes.
In Mikolajczyk et al., six region detectors are studied. A summary of MSER performance in comparison to the other five follows.
Note however that this evaluation did not make use of multi-resolution detection, which has been shown to improve repeatability under blur.
MSER consistently resulted in the highest score through many tests, proving it to be a reliable region detector.

Implementation

The original algorithm of Matas et al. is in the number of pixels. It proceeds by first sorting the pixels by intensity. This would take time, using BINSORT. After sorting, pixels are marked in the image, and the list of growing and merging connected components and their areas is maintained using the union-find algorithm. This would take time. In practice these steps are very fast. During this process, the area of each connected component as a function of intensity is stored producing a data structure. A merge of two components is viewed as termination of existence of the smaller component and an insertion of all pixels of the smaller component into the larger one. In the extremal regions, the 'maximally stable' ones are those corresponding to thresholds where the relative area change as a function of relative change of threshold is at a local minimum, i.e. the MSER are the parts of the image where local binarization is stable over a large range of thresholds.
The component tree is the set of all connected components of the thresholds of the image, ordered by inclusion. Efficient algorithms for computing it do exist. Thus this structure offers an easy way for implementing MSER.
More recently, Nister and Stewenius have proposed a truly worst-case method in, which is also much faster in practice. This algorithm is similar to the one of Ph. Salembier et al.

Robust wide-baseline algorithm

The purpose of this algorithm is to match MSERs to establish correspondence points between images. First MSER regions are computed on the intensity image and on the inverted image. Measurement regions are selected at multiple scales: the size of the actual region, 1.5x, 2x, and 3x scaled convex hull of the region. Matching is accomplished in a robust manner, so it is better to increase the distinctiveness of large regions without being severely affected by clutter or non-planarity of the region's pre-image. A measurement taken from an almost planar patch of the scene with stable invariant description are called a 'good measurement'. Unstable ones or those on non-planar surfaces or discontinuities are called 'corrupted measurements'. The robust similarity is computed:
For each on region regions from the other image with the corresponding i-th measurement nearest to are found and a vote is cast suggesting correspondence of A and each of. Votes are summed over all measurements, and using probability analysis, 'good measurements' can be picked out as the 'corrupt measurements' will likely spread their votes randomly. By applying RANSAC to the centers of gravity of the regions, a rough epipolar geometry can be computed. An affine transformation between pairs of potentially corresponding regions is computed, and correspondences define it up to a rotation, which is then determined by epipolar lines. The regions are then filtered, and the ones with correlation of their transformed images above a threshold are chosen. RANSAC is applied again with a more narrow threshold, and the final epipolar geometry is estimated by the eight-point algorithm.
This algorithm can be tested here :

Use in text detection

The MSER algorithm has been used in text detection by Chen by combining MSER with Canny edges. Canny edges are used to help cope with the weakness of MSER to blur. MSER is first applied to the image in question to determine the character regions. To enhance the MSER regions any pixels outside the boundaries formed by Canny edges are removed. The separation of the later provided by the edges greatly increase the usability of MSER in the extraction of blurred text.
An alternative use of MSER in text detection is the work by Shi using a graph model. This method again applies MSER to the image to generate preliminary regions. These are then used to construct a graph model based on the position distance and color distance between each MSER, which is treated as a node. Next the nodes are separated into foreground and background using cost functions. One cost function is to relate the distance from the node to the foreground and background. The other penalizes nodes for being significantly different from its neighbor. When these are minimized the graph is then cut to separate the text nodes from the non-text nodes. To enable text detection in a general scene, Neumann uses the MSER algorithm in a variety of projections. In addition to the greyscale intensity projection, he uses the red, blue, and green color channels to detect text regions that are color distinct but not necessarily distinct in greyscale intensity. This method allows for detection of more text than solely using the MSER+ and MSER- functions discussed above.

Extensions and adaptations