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Sub-Pixel Accuracy for Matched Filter Alignment System

IP.com Disclosure Number: IPCOM000122213D
Original Publication Date: 1991-Nov-01
Included in the Prior Art Database: 2005-Apr-04
Document File: 5 page(s) / 119K

Publishing Venue

IBM

Related People

Polkowski, E: AUTHOR

Abstract

A method has been proposed so that an image processing alignment system may locate a desired pattern to within + 1 pixel. The method is an extension of the matchbox alignment algorithm [*].

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 52% of the total text.

Sub-Pixel Accuracy for Matched Filter Alignment System

      A method has been proposed so that an image processing
alignment system may locate a desired pattern to within + 1 pixel.
The method is an extension of the matchbox alignment algorithm [*].

      The matchbox alignment system uses a matched filter algorithm
expressed by:
      Pxy(ki) = MAX[   Rxy  (k)   ]      (1)
                                    K where:
                   N-1
      Rxy(k) = 1/N S X(n)Y(n-k)               (2)
                   n=0
and:  Rxy(k) = the cross-correlation of signals X and Y at k
       N = the number of samples
       X(n) = the input signal
       Y(n) = the reference signal

      The foregoing equation is the discrete form of the
cross-correlation function for N points.  It results in a sequence of
numbers for O<k<N-1 which represents the similarity of the input
signal with the reference signal. The value of k at which Rxy(k) is a
maximum is the alignment point.  This technique provides an accuracy
of + samples.

      In the proposed technique which will provide sub-sample
accuracy, it is assumed that all spatial features viewed by the
system will be of such dimensions that all significant spatial
frequencies created by the features will be under 1/2 the spatial
sampling rate.

      As an example, a vision sensor creates an analog signal (Fig.
1) based on a viewed scene where the ordinate Vs is the sensor
voltage and t = time.  The alignment problem is to locate the peak 1
of the signal so as to locate a bright feature in the viewed scene.
For digital processing the image will be sampled every T seconds and
stored.  Or the signal may already be in sampled form if obtained
from a solidstate sensor with defined pixel geometry.

      The sample data is plotted in Fig. 2 with the peak at t6 .
The actual peak, as it occurs in Fig. 1, is between t5 and t6 .
The resolution is + sample with it known that the peak will be
located between samples t5 and t7 .

      It is possible to obtain a better resolution by interpolating
signal values between the actual samples using an ideal filter, as
depicted in Fig. 3.
where:  fs = 1/T = sampling rate
with impulse response h(t) = sync fst,
the reconstructed signal is given by:
           B
      y(t) = S x (nT) sinc(fst-n)        (3)
           n=B

      The signal may be calculated for M points between t5 and t6 and
M points between t6 and t7 . ...