Abstract

This paper considers the problem of mathematically eliminating a nonuniform rectilinear smear in an image, for example, a picture taken by a motionless camera of runners on a track, running at different speeds. The problem is described by a set of one-dimensional integral equations of a general type (not a convolution type) with a two-dimensional point scattering function or one two-dimensional integral equation with a four-dimensional point scattering function. The integral equations are solved by Tikhonov regularization and quadrature/cubature. It is shown that, in the case of a nonuniform smear, the use of a set of one-dimensional integral equations is preferable to one two-dimensional integral equation. In the direct problem, the image smear is supplemented by truncating it, evading the boundary conditions, and diffusing its edges to suppress the Gibbs effect in the inverse problem. Cases of piecewise uniform and continuously (linearly) nonuniform smear are considered. Illustrative results are presented.

© 2020 Optical Society of America

Restoration and frequency analysis of smeared CCD images

Keith Powell, Deeph Chana, David Fish, and Chris Thompson
Appl. Opt. 38(8) 1343-1347 (1999)

Restoration of a smeared photographic image by incoherent optical processing

F. T. S. Yu
Appl. Opt. 17(22) 3571-3575 (1978)

Incoherent processor for restoring images degraded by a linear smear

L. Celaya and S. Mallick
Appl. Opt. 17(14) 2191-2197 (1978)

Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time

Ting Sun, Fei Xing, Zheng You, Xiaochu Wang, and Bin Li
Opt. Express 22(5) 6009-6024 (2014)

Analysis of the Effect of Linear Smear on Photographic Images*

S. C. Som
J. Opt. Soc. Am. 61(7) 859-864 (1971)