A particle detector for spotlike structures (bright on dark background) in 2D based on the undecimated wavelet transform.
The undecimated wavelet transform produces wavelet coefficient images that correspond to the results of filtering the original image with a bank of filters.
There is one lowpass-filtered image, one highpass-filtered image and several bandpass filtered images, depending on the parameter Jmax. The different bands/filtered images are referenced by the scale.
The parameters Jmin and Jmax determine the lower and upper scale limit and thus control the range of wavelet images that are taken into account for particle detection. Scale 1 corresponds to the highpass filtered image and increasing scales correspond to decreasing frequency bands.
The Scale-interval size parameter determines, how many wavelet images of adjacent scales are used to compute a wavelet correlation image, which is the multiplication of wavelet coefficients over adjacent scales at each pixel.
A short example:
Jmin=2, Jmax=4, Scale-interval size=2. That means that the bandpass filtered images of scale 2 and 3 are multiplied for one correlation image, and the bandpass filtered images of scale 3 and 4 for another.
Correlation images are then thresholded by Correlation threshold to yield hypotheses of particle detections.
Because multiple hypotheses can exist at the same location due to multiple correlation images, a kind of hypothesis testing is used to determine the more likely detection at a certain location.
The resulting particle detections can be extracted from the particle detector as a set of regions.
The input image may be transformed if it contains Poisson noise to simulate Gaussian noise
For more details see O. Gress, B. Möller, N. Stöhr, S. Hüttelmaier, S. Posch, "Scale-adaptive wavelet-based particle detection in microscopy images". In Proc. Bildverarbeitung für die Medizin (BVM 2010), pages 266-270, March 2010, Springer.
Input image:
Image where particles have to be detected
Jmin:
Minimum scale (integer value > 1)
Jmax:
Maximum scale (integer value > Jmin > 1)
Scale-interval size:
Size of scale-interval to be merge scales to wavelet correlation images (integer value <= Jmax-Jmin+1)
Correlation threshold:
Threshold for thresholding wavelet correlation images (real value > 0)
Minimum region size:
The minimum size of that a detected region must have
Poisson- to Gaussian noise transform:
Flag to transform Poisson to Gaussian noise
Resulting regions
The set of regions representing detected particles