Noise Reduction and Segmentation Techniques Developed for Multidimensional Electron Microscopy of Biological Specimens

Computed tomography techniques are the most widely applicable non-invasive methods for giving unique insights into the three dimensional (3D) organization of pleomorphic biological objects. Recent advances in the recording schemes improve the speed and resolution and provide new insights into the structural organization of different specimens. The boundaries in the applicability are set by dose limitation, limited accessibility of the data and resolution. In electron tomography the resolution limits are improved down to 2-4 nm, which should allow the identification of large biological macromolecules in their native environment. However the low signal to noise ratio hinders the application of image processing methods for data analysis, such as visualization, segmentation and feature extraction. In this thesis four image processing techniques have been developed and implemented in the field of electron microscopy in order to improve the performance in terms of signal reconstruction, processing time and visualization. A new noise reduction (denoising) technique is proposed based on nonlinear anisotropic diffusion. Diffusion methods for signal reconstruction became widely applicable due to their well-established mathematical properties and their general well posedness. Several different methods have been proposed mainly focused on edge detection and edge preservation, but none of them became applicable for highly degraded data. A new hybrid approach has been developed, which combines conventional diffusion methods and overcomes the handicaps of the present realizations. This diffusion technique shows a superior performance as compared to existing diffusion realizations, as well as to conventional methods typically applied in image processing (e.g. low pass filtering, median filtering) and invariant wavelet filtering. Several quantitative measures to assess the signal reconstruction performance have been established. The best reconstruction performance is observed at spatial frequencies lower than half of the Nyquist frequency. The method is therefore appropriate for the mostly oversampled electron microscopic data. The signal to noise ratio improvement is demonstrated by means of Fourier shell correlation functions. Several examples demonstrating the significant improvement of the visualization quality of the data sets are presented. Additionally the method proves to be an excellent preprocessing step for object detection and segmentation techniques. Mean curvature motion is a novel approach for object detection. It is a nonlinear anisotropic diffusion process, where the diffusion flux is explicitly set to zero in the direction of the gradient. As the level sets of the image (isointensity contours) move as a function of their own curvature, they degrade to concave regions and disappear to singularities, which can be detected a posteriori indicating the position of a feature. This method can be applied as a preprocessing step for object detection in two-dimensions (2D) as well as in 3D is robust with respect to noise (for a signal to noise ratio larger than 0.1) and rotational and translation invariant. Additionally is also a parameter-free method since the only parameter, which has to be determined (iteration time) depends directly on the size of the feature to be identified. An extended performance evaluation on real and artificial data, as well as with an interactively selected data set is presented. Automatic grouping and segmentation is a challenging problem in the image-processing field. The main goal of image segmentation is an image simplification, such that the interesting parts of the image are separated from each other and the effective size of the image reduces to the substantial part. Decreasing of the effective processing size and improvement of the visualization capabilities are the two most important effects of each segmentation technique. A segmentation procedure is in general not objective, as compared when different individuals perceive distinct features as the important objects in the image. Two techniques covering a broad field have been developed, the active contours as an interactive segmentation tool and an eigenvector based approach for automated image analysis. The "snake" segmentation based on the movement of an active contour towards a detectable boundary has been applied at various image processing applications. Nevertheless, due to the missing wedge, the low signal to noise ratio and the pleomorphic features is not directly applicable for interactive segmentation in the field of electron microscopy. A modification of the partial differential equations is proposed in order to block the level set movement in the direction of the missing information. The technique remains very sensitive to the initial conditions and is therefore not applicable for automated segmentation. Interactively the user has the option to determine an arbitrary boundary, near to the object of interest, which will be approached by the snake in a finite time. Application examples in 2D and 3D are presented. The use of eigenvectors for segmentation of multidimensional images in the field of electron microscopy is a novel approach. With the use of the second smallest eigenvector of an affinity matrix containing similarity measures between the pixels a foreground/background separation is attained. Several similarity measures e.g. distance, gray value, texture can be implemented in the algorithm. The most dominant feature in the image could be always automatically segmented improving the visualization significantly. The parameter choice turns out to be very robust, making the method widely applicable for various 2D and 3D electron microscopic images.