Certain situations, for instance in flat-panel cone beam CT, permit that only a relatively low number of projections are acquired. The reconstruction quality of the volume to be imaged is then compromised by streaking artifacts. To avoid these degradations, additional projections are interpolated between the genuinely
acquired ones. Since straightforward linear, non-adaptive interpolation generally results in loss of sharpness, techniques were developed which adapt to, e.g., local orientation within the sinogram. So far, such directional interpolation algorithms consider only single local orientations. Especially in x-ray imaging,
however, different non-opaque orientated structures may be superimposed. We therefore show how such multiply-oriented structures can be detected, estimated, and included in the interpolation process. Furthermore, genuine sinograms meet certain conditions regarding their moments as well as regarding their
spectra. Moments of 2D sinograms depend on the projection angle in the form of sinosoids, while the Fourier spectrum of the sinogram takes the form of a 'bow tie'. The consistency of the interpolated data with these conditions may therefore be viewed as additional measures of the interpolation quality. For linear interpolation, we analyze how well the interpolated data comply with these constraints. We also show how the moment constraint can be
integrated into the interpolation process.
We first review theoretical results for the problem of estimating single and multiple transparent motions. For N motions
we obtain a M×M generalized structure tensor J<sub>N</sub> with M = 3 for one, M = 6 for two, and M = 10 for three motions.
The analysis of motion patterns is based on the ranks of J<sub>N</sub> and is thus not only conceptual but provides computable
confidence measures for the different types of motions. To resolve the correspondence between the ranks of the tensors
and the motion patterns, we introduce the projective plane as a new way of describing motion patterns. In the projective
plane, intrinsically 2D spatial patterns (e.g. corners and line ends) that move correspond to points that represent the only
admissible velocity, and 1D spatial patterns (e.g. straight edges) that move correspond to lines that represent, as a set
of points, the set of admissible velocities. We then show a few examples for how the projective plane can be used to
generate novel motion patterns and explain the perception of these patterns. We believe that our results will be useful
for designing new stimuli for visual psychophysics and neuroscience and thereby contribute to the understanding of the
dynamical properties of human vision.
This paper deals with the problem of estimating multiple motions at points where these motions are overlaid. We present a new approach that is based on block-matching and can deal with both transparent motions and occlusions. We derive a block-matching constraint for an arbitrary number of moving layers. We use this constraint to design a hierarchical algorithm that can distinguish between the occurrence of single, transparent, and occluded motions and can thus select the appropriate local motion model. The algorithm adapts to the amount of noise in the image sequence by use of a statistical confidence test. The algorithm is further extended to deal with very noisy images by using a regularization based on Markov Random Fields. Performance is demonstrated on image sequences synthesized from natural textures with high levels of additive dynamic noise.
This paper deals with the problem of estimating multiple transparent
motions that can occur in computer vision applications, e.g. in the
case of semi-transparencies and occlusions, and also in medical
imaging when different layers of tissue move independently. Methods
based on the known optical-flow equation for two motions are
extended in three ways. Firstly, we include a regularization term
to cope with sparse flow fields. We obtain an Euler-Lagrange system
of differential equations that becomes linear due to the use of the
mixed motion parameters. The system of equations is solved for the
mixed-motion parameters in analogy to the case of only one motion.
To extract the motion parameters, the velocity vectors are treated
as complex numbers and are obtained as the roots of a complex
polynomial of a degree that is equal to the number of overlaid
motions. Secondly, we extend a Fourier-Transform based method
proposed by Vernon such as to obtain analytic solutions for more
than two motions. Thirdly, we not only solve for the overlaid
motions but also separate the moving layers. Performance is
demonstrated by using synthetic and real sequences.