The horizontal size of a particle is defined as the distance from the left-most to the right-most pixel contained within the particle. This option allows a lower limit to be placed on this size. The limit acts independently of [R Lower size limit]: a blob must satisfy both criteria to be accepted as a particle.
The purpose behind imposing a minimum horizontal particle size is based on the desire to know the location of the particles with subpixel accuracy. Clearly if a particle occupies only one pixel in the horizontal direction, then its position may only be determined with pixel accuracy. However, if the particle occupies more than one pixel, then the intensity information may allow us to determine its location to better than pixel accuracy.
We shall illustrate this with a simplified example. Consider a particle two pixels in width and suppose the real intensity is uniform across the width of the particle. Now if the particle were aligned exactly with the pixels, then it would occupy a width of exactly two pixels, each of which would have the same intensity. If instead the particle were centred on one pixel, then it would appear to occupy three pixels in the digitized image: the centre pixel would have an intensity equal to that of the particle, while the outer two would have approximately half that intensity. The position of the particle in this situation would correspond to both the centroid of the area and the centroid of the volume (see [C Area/Volume centroid]).
The reason for the minimum particle width and the use of the volume centroid becomes more apparent if the particle is positioned so that it covers some fraction f (f<1) of the left-hand pixel, all the middle pixel and a fraction 1-f of the right-hand pixel. With an ideal camera, video tape and digitizer response, and assuming a black background, the intensities of the pixels will be f, 1 and 1-f respectively. The area centroid will still give the particle location as the centre of the middle pixel, while the volume centroid will give the particles true position.