What is Maximally Stable Extremal Regions (MSER)?

Question

In the paper Robust wide-baseline stereo from maximally stable extremal regions , MSER is being defined. Please help me understand what is MSER and how to implement it. The paper says,

The regions are defined solely by an extremal property of the intensity function in the region and on its outer boundary.

1. What do mean by extremal and intensity function? What kind of intensity function is the paper referring to?

2. According to the paper,

The concept can be explained informally as follows. Imagine all possible thresholds of a gray-level image I: We will refer to the pixels below a threshold as ‘black’ and to those above or equal as ‘white’. If we were shown a movie of thresholded images It; with frame t corresponding to threshold t; we would see first a white image. Subsequently black spots corresponding to local intensity minima will appear and grow. At some point regions corresponding to two local minima will merge. Finally, the last image will be black. The set of all connected components of all frames of the movie is the set of all maximal regions; minimal regions could be obtained by inverting the intensity of I and running the same process.

I could not picture out the things the author wants to relay. Can anyone describe it to me in simple terms or a demonstration will also do. Formal definition of MSER is shown in the image below.

Answer 1

You can see this using 1d path:

stable region is where change of the threshold does not change the area of the region. so its contrast it relatively high.

look at the surface of the image

the stepper the boundary the more stable the region is.

Images from University of Washington - CSE455: Computer Vision - MSER Operator: Maximally Stable Extremal Regions and matlab.