Level set methods are a popular way to solve the image segmentation problem. The solution contour is found by solving an optimization problem where a cost functional is minimized. Gradient descent methods are often used to solve this optimization problem since they are very easy to implement and applicable to general nonconvex functionals. They are, however, sensitive to local minima and often display slow convergence. Traditionally, cost functionals have been modified to avoid these problems. In this paper, we instead propose using two modified gradient descent methods, one using a momentum term and one based on resilient propagation. These methods are commonly used in the machine learning community. In a series of 2-D/3-D-experiments using real and synthetic data with ground truth, the modifications are shown to reduce the sensitivity for local optima and to increase the convergence rate. The parameter sensitivity is also investigated. The proposed methods are very simple modifications of the basic method, and are directly compatible with any type of level set implementation. Downloadable reference code with examples is available online.

/pdf/modified-gradient-search-for-level-set-based-image-3nvkr7ka7g.pdf

Modified Gradient Search for Level Set Based Image Segmentation

We present a hierarchical Markov Random Field (HMRF) for multi-label image segmentation. With such a hierarchical model, we can incorporate global knowledge into our segmentation algorithm. Solving the MRF is formulated as a MAX-SUM problem for which there exist efficient solvers based on linear programming. We show that our method allows for automatic segmentation of mast cells and their cell organelles from 2D electron microscopic recordings. The presented HMRF outperforms classical MRFs as well as local classification approaches wrt. pixelwise segmentation accuracy. Additionally, the resulting segmentations are much more consistent regarding the region compactness.

Hierarchical Markov Random Fields for mast cell segmentation in electron microscopic recordings

In life-sciences, technical innovations in microscopy and the ever growing availability of modern fluorescence microscopes allow for the investigation of more and more complex biological processes. To facilitate the analysis of the recorded microscopic data, the development of automated methods is indispensable, because these methods allow for the evaluation of a sufficient amount of data without bias. The analysis of fluorescence microscopic data comes with some specific challenges. The recorded fluorescence signal is noisy, the signal intensity of the identical structure potentially varies from one recording point to the other and the recording resolution is strongly anisotropic due to technical limitations. Additionally, the optical system introduces blur, which is commonly described by a convolution with the so called point spread function. The presented thesis primarily focuses on the segmentation of objects, mostly cells, cell nuclei, or other cell organelles, from microscopic recordings. Another key aspect is the deconvolution of the recordings in order to alleviate the blur introduced by the optical system. Especially when processing data from widefield microscopy, deconvolution is often a crucial preprocessing step. The presented methods for blind deconvolution are based on the regularization of the reconstructed point spread function. On our test datasets, they lead to improved, sharpened images with a better signal to noise ratio. A comparison to state-of-the-art methods confirms the aptitude of our approach. The proposed methods for the segmentation of objects from volumetric data are based on parametric active surfaces. An important contribution is the generation of appropriate data terms for the representation of the object boundaries in noisy data with weak fluorescence signal. Thus, we present methods for the generation of data terms that allow for the segmentation of fluorescently labeled cell nuclei and nucleoli from widefield microscopic recordings. Furthermore, we propose a method to automatically generate new, very specific data terms for the segmentation of objects from volumetric data based on very simple user input. Experiments show that our methods allow an accurate segmentation of the objects under investigation, which, with conventional active surface and level set methods, could not be achieved. Thereby, our dataterms can be easily adapted to changing recording conditions. Finally, we present a method that allows to learn topological knowledge that can be used for the simultaneous classification and segmentation of objects. This approach is based on hierarchical Markov Random Fields. By means of this method, the segmentation accuracy in a dataset of electron microscopic recordings could be greatly improved compared to conventional Markov Random Fields.

Segmentation of Cells and Sub-cellular Structures from Microscopic Recordings

Biological images have the potential to reveal complex signatures that may not be amenable to morphological modeling in terms of shape, location, texture, and color. An effective analytical method is to characterize the composition of a specimen based on user-defined patterns of texture and contrast formation. However, such a simple requirement demands an improved model for stability and robustness. Here, an interactive computational model is introduced for learning patterns of interest by example. The learned patterns bound an active contour model in which the traditional gradient descent optimization is replaced by the more efficient optimization of the graph cut methods. First, the energy function is defined according to the curve evolution. Next, a graph is constructed with weighted edges on the energy function and is optimized with the graph cut algorithm. As a result, the method combines the advantages of the level set method and graph cut algorithm, i.e., topological invariance and computational efficiency. The technique is extended to the multi-phase segmentation problem; the method is validated on synthetic images and then applied to specimens imaged by transmission electron microscopy(TEM).

Structural annotation of em images by graph cut

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Structural annotation of em images by graph cut