Research of the MIA Group

We perform research on mathematically well-founded methods in image processing and computer vision. The main focus is on techniques based on partial differential equations and variational methods, but also morphological methods, wavelets and nonlocal filters are used. We are interested in all aspects of these techniques, including mathematical modeling, well-posedness analysis, efficient algorithms for sequential and parallel computer architectures, and a multitude of applications.

Image Processing – Computer Vision – Scientific Computing – Applications

Diffusion Filtering

Noisy imagery constitutes a very frequent problem, appearing e.g. in digital images that have been acquired under poor illumination conditions, or in ultrasound images arising in medical imaging. Thus, one of the most important problems ...

Mathematical Morphology

Mathematical morphology originated from the study of porous media in the mid-sixties. Since then it has undergone a tremendous development resulting in efficient tools for modern image processing and analysis ...

Relations between Denoising Methods

We consider a classical task of signal denoising: create an estimate u of an original signal z from its noisy measurement f, where f = z + n and n denotes an additive noise function ...

Deblurring Methods

Blur in image data hampers the utilisation of image acquisition methods in many fields of application. Deconvolution methods allow to enhance such image data ...

Halftoning

Many devices such as printers and fax machines can often create only pure black and white images. To represent intermediate grey values, it is necessary to virtually increase the range of such devices by using a halftoning algorithm. ...

Inpainting-Based Image Compression

Image compression methods that base on image inpainting based on partial differential equations (PDEs) constitute a relatively novel class of lossy image compression methods. They can build the basis for future alternatives to standards such as JPEG or JPEG 2000. ...

Image Processing of Tensor Fields

Matrix-valued data sets (so-called tensor fields) are gaining increasing importance in digital imaging. In our group we have developed a number of novel image processing methods that work directly on tensor fields ...

Optic Flow

Correspondence problems are one of the key problems in computer vision. They appear for example in motion analysis, image matching, or stereo vision. The goal is to assign structures in one image to structures in a second image, in a way that corresponding structures are as similar as possible ...

Stereo Reconstruction

The goal of dense stereo vision is to reconstruct realistic 3D models from two or more stereo images. In its most elementary setup, stereo vision is closely related to the optical flow problem between two images. Compared to pure optical flow, the motion of the pixels in a stereo setting is additionally restricted by the geometry of the image pair, the so called epipolar geometry. ...

Scene Flow

Scene flow denotes the real 3-D motion of objects in the scene, as opposed to optical flow, which only describes the projection of this motion on the 2-D image plane. In contrast to structure from motion, where a single camera moves through a static environment, ...

Shape from Shading

Shape from Shading (SfS) means recovering a three-dimensional surface from the shading information contained in a two-dimensional image under known illumination conditions and reflectance properties of the surface. ...

Pose Tracking

3-D pose tracking is the task to follow the 3-D position and orientation of a known object through a video sequence. There are a multitude of applications for which pose tracking is necessary, such as self localization and object grasping in robotics, motion capture, or human computer interaction. ...

Image Segmentation

The partitioning of an image into meaningful regions is one of the principal computer vision tasks. On the way from the raw pixel data up to a meaning of the image, it is necessary to reduce the amount of information and to represent it in a compact manner...

Semidiscrete Analysis and Numerics of Diffusion Processes

Diffusion filters of image analysis are modelled and analysed in a semidiscrete setting. Stability and convergence of numerical schemes can be analysed in this way, and interesting new numerical schemes can be derived ...

Hyperbolic Schemes

There are many models in image processing and computer vision that employ hyperbolic partial differential equations. Of particular interest for image processing and computer vision task are economic schemes with high shock resolution that result in sharp edges. We construct new finite difference schemes for this purpose. ...

Fast Explicit Diffusion

There are two popular ways to implement anisotropic diffusion filters with a diffusion tensor: Explicit finite difference schemes are simple but become inefficient due to severe time step size restrictions, while semi-implicit schemes are more efficient but require to solve large linear systems of equations. We present a novel class of algorithms that combine the advantages of both worlds ...

Additive Operator Splittings

An efficient numerical approach for the acceleration of algorithms is the use of so called splitting schemes. They decompose a complicated problem into multiple problems that are numerically simpler. So-called additive operator splittings (AOS) offer specific advantages over the widely-used multiplicative splittings. ...

Multigrid Methods

Multigrid methods are among the fastest and most accurate numerical schemes for the solution of linear and nonlinear system of equations. They create a sophisticated coarse-to-fine hierarchy starting from the original equation system. Very accurate results are already obtained within a few iterations. ...

Efficient Parallel Algorithms

For certain problems the use of sophisticated numerical schemes may still not be sufficient to obtain the desired performance. At this point, one should consider the development of efficient parallel algorithms that are tailored ...

Algorithms for Specific Hardware

Modern consumer hardware offers new opportunities. We develop cell phone adaptations of our algorithms and exploit fast parallel hardware like graphics cards or the PlayStation 3 video console to obtain substantial speedups. ...

Movie Processing

In the times of digital media, the processing of video sequences and movies becomes more important every year. A particular challenge in the context of video processing is the fact that objects typically move between subsequent frames ...

Medical Image Analysis

Medical image analysis is one of the main application fields for novel digital image processing methods. We have explored a number of applications that serve as demonstrators for our methods for image denoising, structure enhancement, segmentation and classification. ...

Bioinformatics and Systems Biology

The rapid progress within the areas of bioinformatics and systems biology gives rise to numerous image analysis problems. We collaborate with a number of researchers at Saarland University and other research institutes in order to address these problems. ...

Computer Aided Quality Control

Quality control in industrial production is a key factor for the success of the products. In order to achieve uniform quality standards, automisation using machine vision methods is becoming more and more important. Often real-time requirements create algorithmic challenges. ...

Information Security and Cryptography

Information security and cryptography play a major role in the digital age. Images as confidential information constitue a special type of messages. This allows adapted attacks and on the other side opens the door to novel cryptographic applications. ...

Beauty and Wellness

Beauty and wellness are areas where one usually would not expect applications from digital image processing and computer vision. However, our research shows that these fields offer an interesting, so far unexplored potential. ...

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