Pde-based image and structure enhancement for electron tomography of mitochondria

Mitochondrial function plays an important role in the regulation of apoptosis. Additionally, defects in this function are believed to be related to many common diseases of aging. In the presence of one of these diseases, mitochondrial function undergoes measurable disturbance accompanied by drastic morphological alterations, suggesting that a correlation exists between mitochondrial structure and functionality. However, the interpretation and measurement of the architectural organization of mitochondria depend heavily upon the availability of good software tools for filtering, segmenting, extracting, measuring, and classifying the features of interest. In this work, we develop mathematically sound and computationally robust partial differential equation-based algorithms for the reduction of noise, and the enhancement of structural information in images of mitochondria obtained via electron microscope tomography. We design a multi-stage approach for extracting the mitochondrial structures from electron tomograms. For the noise reduction phase of the pipeline, we devise a structure enhancing anisotropic nonlinear diffusion model. It is based on an improved image smoothing and edge detection technique that employs a combination of nonlinear diffusion and bilateral filter. The eigenvectors of the bilaterally smoothed structure tensor form the basis for the diffusion tensor, where the eigenvalues are prescribed so that there is a smooth transition, rather than a hard threshold switching, of the diffusion characteristics among image areas of differing structural properties. The method is equipped with a new and simple diffusion stopping criterion, derived from the second derivative of the correlation between the noisy image and filtered image. After the noise reduction phase, we synthetically enhance the contrast of the image by applying the confidence connected segmentation algorithm. Following that, structures are extracted using a level set formulation which includes a term that drives the level set function toward a signed distance function. The extracted contours are rendered as a three-dimensional image model. The results are very encouraging and this computational approach is potentially much faster, and is more robust and unbiased than hand-tracing of structures. We develop an adaptive total variation-based model with morphologic convection and anisotropic diffusion, and devise a user-independent method for choosing all the parameters in the model. We estimate the unknown noise level via a simple approximation that uses convolution with a Gaussian kernel. We implement a pixel-wise parameter in the forcing-term that allows more diffusion in homogeneous areas, and it restricts the diffusion in areas with higher probability of belonging to edges. This parameter also enables more diffusion in the early stages of the scale-marching process and discourages diffusion as iterations evolve. For the anisotropic diffusion process, we implement a diffusion tensor that adapts to the underlying structure of the image by applying a range of diffusion processes in each direction. The proposed model applies diffusion methods consistent with either the total variation-norm or the Euclidean-norm, or an interpolation between these two norms. We also implement an adaptive time-step that helps with the stability and the speed of the total variation-based restoration process. The adaptive time-step is smaller in regions with high gradients and is larger in regions with low gradients. The results obtained by applying this model to noisy images are comparatively superior in both speed and quality of the restoration. We propose a homomorphic total variation-based algorithm for the reduction of the multiplicative noise present in low-dose electron microscope imagery. In the implementation of this model we employ some of the aforementioned adaptive parameters that we devise for the adaptive total variation-based model. We compare the performance of the proposed model to that of a total variation-based algorithm that was originally designed for the removal of multiplicative noise. The resulting images after applying both techniques are very similar in quality. Ours is the first implementation of this method within the context of electron microscope tomography.