We describe an algorithm for registering spectral images acquired by a pushbroom multispectral scanner operating on an airborne or spaceborne platform subject to uncontrolled motion, i.e., variable time-dependent attitude (pitch, roll, and yaw) and platform position. In contrast to imagery collected during straight and level flight, uncontrolled platform motion causes each band to be warped with respect to the others. The warped bands cannot be simply registered using a rigid transformation but instead require a space-varying de-warping transformation. However, determination of this de-warping transformation from image data remains a challenging problem. In this paper, we formulate a powerful yet efficient model for the warp that takes into account both the detector array geometry and the imaging geometry. The physically-based geometric constraints incorporated into the model enable it to distinguish effectively between image-to-image warp due to uncontrolled variations in the sensor line-of-sight and band-to-band variations in image content and measurement noise. Results show that the model is capable of recovering the true warp in areas where there is little or no correlation in spatial content between the bands. For the test cases studied, the spline-warp model is able to reduce the registration error in the local warp determined from data using image correlation techniques by more than an order of magnitude.
The sharpness of a printed image may suffer due to the presence of
material layers above and below the dye layers. These layers
contribute to scattering and surface reflections that make the
degradation in sharpness density-dependent. We present data that
illustrate this effect, and model the phenomenon numerically. A
digital non-linear sharpening filter is proposed to compensate for
this density-dependent blurring. The support and shape of this
filter is constrained to lie in a space spanned by a set of basis
filters that can be computed efficiently. Burt and Adelson's
Laplacian pyramid is used to develop an efficient scale-recursive
algorithm in which the image is decomposed into the high-pass basis images in a fine-to-coarse scale sweep, and the sharpened image along with a local density image is subsequently synthesized by a coarse-to-fine scale sweep using these basis images. The local density image is employed, in combination with a scale dependent gain function, to modulate the high-pass basis images in a space-varying fashion. A robust method is proposed for the estimation of the gain functions directly from measured data. Experimental results demonstrate that the proposed algorithm successfully compensates for media-related density dependent blurring.
As printing proceeds in a thermal printer, heat from previously printed lines of image data accumulates in the print head and alters the thermal state of the heating elements. This fluctuating state of the heating elements manifests itself as a distortion in the printed image. We have modeled the heat diffusion within the thermal printer and the density response of the receiver medium to derive a computationally efficient inverse thermal printer model. In this model, the heat diffusion problem for the moving receiver is simplified by showing that it is equivalent to a stationary medium with lower conductivity. The thermal print head is modeled as having a finite number of discrete layers with differing time constants. The layer temperature updates can be decoupled and are time recursive if expressed in relative rather than absolute temperatures, and this decoupling allows the layers to be updated at multiple spatial and temporal resolutions. The inverse printer model then reduces to an elegant algorithm that comprises three interleaved recursions; namely, absolute temperature propagation from coarse-to-fine scale, energy propagation from fine-to-coarse scale and relative temperature update in time. Experimental results demonstrate that the proposed algorithm successfully corrects the distortion produced by thermal printers.
This paper addresses the issue of reconstructing the unknown field of absorption and scattering coefficients from time- resolved measurements of diffused light in a computationally efficient manner. The intended application is optical tomography, which has generated considerable interest in recent times. The inverse problem is posed in the Bayesian framework. The maximum a posteriori (MAP) estimate is used to compute the reconstruction. We use an edge-preserving generalized Gaussian Markov random field to model the unknown image. The diffusion model used for the measurements is solved forward in time using a finite-difference approach known as the alternating-directions implicit method. This method requires the inversion of a tridiagonal matrix at each time step and is therefore of O(N) complexity, where N is the dimensionality of the image. Adjoint differentiation is used to compute the sensitivity of the measurements with respect to the unknown image. The novelty of our method lies in the computation of the sensitivity since we can achieve it in O(N) time as opposed to O(N2) time required by the perturbation approach. We present results using simulated data to show that the proposed method yields superior quality reconstructions with substantial savings in computation.
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