Linear Time Maximally Stable Extremal Regions

In this paper we present a new algorithm for computing Maximally Stable Extremal Regions (MSER), as invented by Matas et al. The standard algorithm makes use of a union-find data structure and takes quasi-linear time in the number of pixels. The new algorithm provides exactly identical results in true worst-case linear time. Moreover, the new algorithm uses significantly less memory and has better cache-locality, resulting in faster execution. Our CPU implementation performs twice as fast as a state-of-the-art FPGA implementation based on the standard algorithm. The new algorithm is based on a different computational ordering of the pixels, which is suggested by another immersion analogy than the one corresponding to the standard connected-component algorithm. With the new computational ordering, the pixels considered or visited at any point during computation consist of a single connected component of pixels in the image, resembling a flood-fill that adapts to the grey-level landscape. The computation only needs a priority queue of candidate pixels (the boundary of the single connected component), a single bit image masking visited pixels, and information for as many components as there are grey-levels in the image. This is substantially more compact in practice than the standard algorithm, where a large number of connected components must be considered in parallel. The new algorithm can also generate the component tree of the image in true linear time. The result shows that MSER detection is not tied to the union-find data structure, which may open more possibilities for parallelization.