Blind data restoration with an extracted filter function.

A method for performing blind deconvolutions on degraded images and data has been developed. The technique uses a power law relation applied to the Fourier transform of the degraded data to extract a filter function. This filter function closely resembles the point-spread function of the system and can be used to restore and enhance higher-frequency content. The process is noniterative and requires only that the point-spread function be space invariant and the transfer function be real. The algorithm has been validated by direct comparisons by use of a pseudoinverse filter with known transfer functions.

Simultaneous motion estimation and filtering of image sequences.

In this paper, we present an algorithm to simultaneously estimate multiple-frame motions and filter image sequences. The relative motion dk(x) between the reference frame s(x) and the kth frame s(x-dk(x)) in the presence of additive white Gaussian noise (AWGN) is estimated using the maximum-likelihood (ML) principle. The reference frame is also filtered in the linear minimum mean square error (LMMSE) sense during the process of motion estimation. Simulation experiments are performed using the affine motion model to illustrate the performance of this method.

A Bayes decision test for detecting uncovered-background and moving pixels in image sequences.

We present a ternary hypothesis test for the detection of stationary, moving, and uncovered-background pixels between two image frames in a noisy image sequence using the Bayes decision criterion. Unlike many uncovered-background detection schemes, our scheme does not require motion estimation for the differentiation between moving pixels and uncovered-background pixels. We formulate the Bayes decision rule using a single intensity-difference measurement at each pixel and using multiple intensity-difference measurements in the neighborhood of each pixel. We quantitatively evaluate our detection algorithm on an image sequence which we have generated and qualitatively on the Trevor White image sequence.

Nonuniform image motion estimation using Kalman filtering.

This correspondence presents a new pixel-recursive algorithm for estimating the nonuniform image motion from noisy measurements. The proposed method is performed in two steps. First, the pixels are examined to identify the (detectable) moving pixels, using a binary hypothesis testing. Then, characterizing the motion of the identified moving pixels in terms of a unitary transformation, the motion coefficients are estimated using a Kalman filter. Because the motion vector is typically (spatially) slowly varying, the size of the motion coefficient vector is significantly reduced. Consequently, the proposed Kalman filter need only search for the truncated coefficients of the motion field. The proposed method is simulated on a computer, and results are compared with the algorithm reported by Netravali and Robbins (see Bell Syst. Tech. J. vol.58, no.3, p.631-70, Mar. 1979).

Nonuniform image motion estimation in reduced coefficient transformed domains.

The transformed domain maximum likelihood (TDML) algorithm for image motion estimation is presented. This algorithm finds a solution which maximizes a log-likelihood function using a steepest ascent scheme. Important characteristics of the algorithm are the inclusion of noise in the signal model, the consideration of motion as a nonuniform process, and calculation of convergence parameters by means of a linear analysis. Simulation on real image sequences demonstrate the validity of the motion estimator. The experiments also verify the validity of the equations presented for the calculation of the convergence parameters. Additional experiments performed to determine the noise sensitivity of the TDML show that noise resistance can be obtained using a reduced coefficient transform (RCT) TDML algorithm. An additional benefit of using an RCT with the TDML algorithm is an increase in the speed of the algorithm without significant performance degradation. Two of the common transforms, Haar and Walsh-Hadamard, are shown to have some interesting properties when utilized with the RCT-TDML algorithm.

On the convergence of the generalized maximum likelihood algorithm for nonuniform image motion estimation.

The generalized maximum likelihood algorithm is a powerful iterative scheme for waveform estimation. This algorithm seeks for the maximum likelihood estimates of the Karhunen-Loeve expansion coefficients of the waveform. The search for the maximum is performed by the steepest ascent routine. The objective of the paper is to obtain conditions that assure the stability in the mean for frame-to-frame image motion estimation. Sufficient conditions are established for the convergence of the algorithm in the absence of noise. Experimental results are presented that illustrate the behavior of the algorithm in the presence of various noise levels.

Nonuniform image motion estimation using the maximum a posteriori principle.

An iterative scheme for frame-to-frame motion estimation from a pair of noisy images is established. The algorithm is developed by assuming that the Karhunen-Loeve coefficients of the motion vector waveform are zero mean and Gaussian random variables. Following the derivation of the generalized maximum likelihood (GML) algorithm, and invoking the maximum a posteriori (MAP) criterion, an iterative motion estimator is developed. A linear analysis of the algorithm is presented, and the convergence of the algorithm is discussed. Simulation experiments are performed and comparisons are made with the GML algorithm the algorithm reported by A.N. Netravali and J.D. Robbins (1979), and the scheme developed by K.P.G. Horn and G.G. Schunck (1981).