Estimation Of Heart Wall Velocity Using The Wigner Distribution

Abstract

The Wigner distribution (WD) has been suggested as an alternative to the Fourier transform as a spatiotemporal-frequency method for measuring optical flow. The WD has the advantage of pixel-by-pixel estimation of the local velocity field in an image set; however, the performance of the WD in estimating apparent local velocity in an nonhomogeneous optical flow field is uncertain. This paper substantiates the high spatial resolution of the WD in estimating the optical flow in an image with a highly nonhomogeneous velocity field. A simple method using linear regression is presented for estimating from the WD the velocity components at a pixel. One of the characteristics of the WD, the lack of a superposition property, gives rise to a cross term in the WD of the sum of 2 image sets that can lead to serious errors in the estimation of optical flow when a simple constant background is added to the image set. These properties are demonstrated with simulated data, and with data from a scintigraphic imaging study of the human heart. The results show that the value of the estimated velocity vector is influenced by the location of the point of inspection. Sketches of the local correlation function for a 1-D moving waveform lend insight into the relationship between the placement of the point of inspection and the estimated velocity.