Department of Image Processing

Authors:  Filip Šroubek, Jan Flusser and Barbara Zitová

Blur is an inevitable, and typically unwanted, phenomenon that is present in all digital images. It results in smoothing high-frequency details, which makes the image analysis difficult. Heavy blur may degrade the image so seriously, that neither automatic analysis nor visual interpretation of the content are possible. There are also situations when the blur is not a nuisance as it conveys information about the source of the blur. For example, motion blur give us hints about the camera and/or object motion. Two major approaches to handling blurred images exist. They are more complementary rather than concurrent; each of them is appropriate for different tasks and employs different mathematical methods and algorithms.

Image restoration is one of the oldest areas of image processing. It appeared as early as in 1960's and 1970's in the work of the pioneers A. Rosenfeld, H. Andrews, B. Hunt, and others. In the last ten years, this area has received new impulses and has undergone a quick development. We have been witnesses of the appearance of multichannel techniques, blind techniques, and superresolution enhancement resolved by means of variational calculus in very high-dimensional spaces. A common point of all these methods is that they suppress or even remove the blur from the input image and produce an image of a high visual quality. However, image restoration methods are often ill-posed, ill-conditioned, and time consuming.

On the contrary, blur-invariant approach, proposed originally in 1995, works directly with the blurred data without any preprocessing. Blurred image is described by features, which are invariant with respect to convolution with some group of kernels. Image analysis is then performed in the feature space. This approach is suitable for object recognition, template matching, and other tasks where we want to recognize/localize objects rather than to restore the complete image. The mathematics behind it is based on projection operators and moment invariants.

In this tutorial, we will focus on both approaches. We start with blur modelling and analyzing potential sources of blur in real images. In the image restoration part of the tutorial we review traditional as well as modern deconvolution techniques, including blind deconvolution, space variant deconvolution, and multichannel deconvolution. The next part covers invariants to image blurring. The tutorial will be completed with numerous demonstrations and practical examples. The tutorial originates from the 20-years speakers' experience in image restoration, deconvolution, invariants, and related fields.

Tutorial slides are available here.