Minimum Vertical Size

Minimum Vertical Size

The vertical size of a particle is defined as the distance from the top-most to the bottom-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 vertical 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 vertical 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, assuming both halves of the interlace contain information at sufficiently close to the same time for the particles not to have moved too far. Consider a particle two pixels in width and suppose the real intensity is uniform across the height of the particle. Now if the particle were aligned exactly with the pixels, then it would occupy a height 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 top pixel, all the middle pixel and a fraction 1-f of the bottom 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.

If the flow is changing so rapidly that one of the interlace filters in [qTI: Interlace filter] has been chosen, or the sample spacing is one video field (in which case an interlace filter will be invoked automatically), then the situation is more complex as the image is only sampled using every second line. It is then necessary for the particle to extend over at least four video lines for it to be located with subpixel accuracy. Unfortunately even then it will not be possible to locate the particles as accurately as it would without the interlace filter due to the combined limitations of quantisation and sampling.

Minimum vertical extent for a paritcle (pixels) ?

This entry specifies the minimum vertical extent a blob must appear to have before it will be considered as a particle. A value of 1 will allow all blobs so long as they satisfy the other criteria, but some of them may be located to only pixel accuracy. To enforce subpixel accuracy, a value greater than one should be specified if no interlace filters are specified (either explicitly or implicitly), or a value greater than three if an interlace filter is to be used. The larger the particles used and the larger the minimum horizontal extent, the more accurately the particle may be located.

If smaller, Ignore or allow only when velocity History ?

If the blob is smaller than the specified lower limit, but still spans at least two pixels (four if an interlace filter is employed) vertically, then we may still wish to consider it as a valid partilce PROVIDED there is a velocity history for it. Responding <H> allows the blob to be considered as a particle (provided there is a velocity history), suffering the [qPR Premium if particle too small] premium. <I> will mean that everything smaller than the limit specified is always ignored. Note that blobs which have insufficient extent and satisfy only the less stringent threshold will always be ignored.

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Stuart Dalziel, last page update: 19 February 1996