In this letter, we consider Suter's DIV-CURL optical flow methods, wherein the Problem of Computing a Velocity field from an image sequence is regularized using smoothness conditions based on the divergence and curl of the Geld. In particular, we develop stochastic formulatiom of DN-CURL splines using the linear smoothing theory of Ad", Willsky, and Levy. Our models are shown to be well posed and thus can be used in both simulating and estimating velocity fields having known stochastic properties. As a special case, our stochastic model reduces to that developed by Rougee, Levy, and Willsky for the classical Horn and Schunck's optical flow.processes. This stochastic model was used by Denney and Psince in [5] and [6] to derive optimal brightness functions for HSOF.In this letter, we first show that Rougee's model is overdetermined, giving a nonphysical model that cannot be used in simulations. We next develop well-posed state-space models for Suter's D W -C W OF methods. Finally, we show that a weu-posed State space model for HSOF is as a special case.
MR tagging has shown great promise for detailed noninvasive cardiac motion imaging. We consider here the use of low-frequency tags coupled with gradientbased optical flow estimation to compute cardiac motion. A multiple constraint optical flow method for tagged MRI is formulated by exploiting the Fourier content of the tagged images. The method is validated on simulated tagged data.&words-optical flow, motion estimation, cardiac tagging.
The routine use of a single radionuclide for patient imaging in nuclear medicine can be complemented by studies employing two tracers to examine two different processes in a single organ, most frequently by simultaneous imaging of both radionuclides in two different energy windows. In addition, simultaneous transmission/emission imaging with dual-radionuclides has been described, with one radionuclide used for the transmission study and a second for the emission study. There is thus currently considerable interest in dual-radionuclide imaging. A major problem with all dual-radionuclide imaging is the "crosstalk" between the two radionuclides. Such crosstalk frequently occurs, because scattered radiation from the higher energy radionuclide is detected in the lower energy window, and because the lower energy radionuclide may have higher energy emissions which are detected in the higher energy window. The authors have previously described the use of Fourier-based restoration filtering in single photon emission computed tomography (SPECT) and positron emission tomography (PET) to improve quantitative accuracy by designing a Wiener or other Fourier filter to partially restore the loss of contrast due to scatter and finite spatial resolution effects. The authors describe here the derivation and initial validation of an extension of such filtering for dual-radionuclide imaging that simultaneously 1) improves contrast in each radionuclide's "direct" image, 2) reduces image noise, and 3) reduces the crosstalk contribution from the other radionuclide. This filter is based on a vector version of the Wiener filter, which is shown to be superior [in the minimum mean square error (MMSE) sense] to the sequential application of separate crosstalk and restoration filters.
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