A major goal of contemporary neuroscience research is to map the structural connectivity of mammalian brain using microscopy imaging data. In this context, the reconstruction of densely labeled axons from two-photon microscopy images is a challenging and important task. The visually overlapping, crossing, and often strongly distorted images of the axons allow many ambiguous interpretations to be made. We address the problem of tracking axons in densely labeled samples of neurons in large image data sets acquired from marmoset brains. Our high-resolution images were acquired using two-photon microscopy and they provided whole brain coverage, occupying terabytes of memory. Both the image distortions and the large data set size frequently make it impractical to apply present-day neuron tracing algorithms to such data due to the optimization of such algorithms to the precise tracing of either single or sparse sets of neurons. Thus, new tracking techniques are needed. We propose a probabilistic axon tracking algorithm (PAT). PAT tackles the tracking of axons in two steps: locally (L-PAT) and globally (G-PAT). L-PAT is a probabilistic tracking algorithm that can tackle distorted, cluttered images of densely labeled axons. L-PAT divides a large micrograph into smaller image stacks. It then processes each image stack independently before mapping the axons in each image to a sparse model of axon trajectories. G-PAT merges the sparse L-PAT models into a single global model of axon trajectories by minimizing a global objective function using a probabilistic optimization method. We demonstrate the superior performance of PAT over standard approaches on synthetic data. Furthermore, we successfully apply PAT to densely labeled axons in large images acquired from marmoset brains.

Tubular shaped networks appear not only in medical images like X-ray-, time-of-flight MRI- or CT-angiograms but also in microscopic images of neuronal networks. We present EMILOVE (Efficient Monte-carlo Image-analysis for the Location Of Vascular Entity), a novel modeling algorithm for tubular networks in biomedical images. The model is constructed using tablet shaped particles and edges connecting them. The particles encode the intrinsic information of tubular structure, including position, scale and orientation. The edges connecting the particles determine the topology of the networks. For simulated data, EMILOVE was able to accurately extract the tubular network. EMILOVE showed high performance in real data as well; it successfully modeled vascular networks in real cerebral X-ray and time-of-flight MRI angiograms. We also show some promising, preliminary results on microscopic images of neurons.

We present a novel method to incorporate prior knowledge into normalized cuts. The prior is incorporated into the cost function by maximizing the similarity of the prior to one partition and the dissimilarity to the other. This simple formulation can also be extended to multiple priors to allow the modeling of the shape variations. A shape model obtained by PCA on a training set can be easily integrated into the new framework. This is in contrast to other methods that usually incorporate prior knowledge by hard constraints during optimization. The eigenvalue problem inferred by spectral relaxation is not sparse, but can still be solved efficiently. We apply this method to biomedical data sets as well as natural images of people from a public database and compare it with other normalized cut based segmentation algorithms. We demonstrate that our method gives promising results and can still give a good segmentation even when the prior is not accurate.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

We present a method for densely computing local rotation invariant image descriptors in volumetric images. The descriptors are based on a transformation to the harmonic domain, which we compute very efficiently via differential operators. We show that this fast voxelwise computation is restricted to a family of basis functions that have certain differential relationships. Building upon this finding, we propose local descriptors based on the Gaussian Laguerre and spherical Gabor basis functions and show how the coefficients can be computed efficiently by recursive differentiation. We exemplarily demonstrate the effectiveness of such dense descriptors in a detection and classification task on biological 3D images. In a direct comparison to existing volumetric features, among them 3D SIFT, our descriptors reveal superior performance.

Accurate identification of protein secondary structures is beneficial to understand three-dimensional structures of biological macromolecules. In this paper, a novel refined classification framework is proposed, which treats alpha-helix identification as a machine learning problem by representing each voxel in the density map with its Spherical Harmonic Descriptors (SHD). An energy function is defined to provide statistical analysis of its identification performance, which can be applied to all the α-helix identification approaches. Comparing with other existing α-helix identification methods for intermediate resolution electron density maps, the experimental results demonstrate that our approach gives the best identification accuracy and is more robust to the noise.

Fiber orientation distributions (FODs) based on diffusion-sensitized magnetic resonance imaging are usually symmetric, primarily due to the nature of the diffusion. In contrast, the underlying fiber configurations are not, as bending or fanning configurations are inherently asymmetric. We propose to dismiss the symmetry of the FOD to additionally encode the asymmetry of the underlying fiber configuration. This is of particular importance for low resolution images that are common in diffusion weighted imaging. We set up the mathematical foundations and geometric interpretations of asymmetric FODs and show how one can benefit from these considerations. We infer a continuity condition that is used as a prior during FOD estimation by constrained spherical deconvolution. This new prior shows superior performance in comparison to other spatial regularization strategies in reliability and accuracy.

The accurate and reliable estimation of fiber orientation distributions, based on diffusion-sensitized magnetic resonance images is a major prerequisite for tractography algorithms or any other derived statistical analysis. In this work, we formulate the principle of fiber continuity (FC), which is based on the simple observation that the imaging of fibrous tissue implies certain expectations for the measured images. From this principle we derive a prior for the estimation of fiber orientation distributions based on high angular resolution diffusion imaging (HARDI). We demonstrate on simulated, phantom, and in vivo data the superiority of the proposed approach. Further, we propose another application of the FC principle, named FC flow, a method to resolve complex crossing regions solely based on diffusion tensor imaging (DTI). The idea is to infer directional information in crossing regions from adjacent anisotropic areas.

In this paper, we present a novel approach for a trainable rotation invariant detection of complex structures in 3D microscopic multichannel data using a nonlinear filter approach. The basic idea of our approach is to compute local features in a window around each 3D position and map these features by means of a nonlinear mapping onto new local harmonic descriptors of the local window. These local harmonic descriptors are then combined in a linear way to form the output of the filter. The optimal combination of the computed local harmonic descriptors is determined in previous training step, and allows the filter to be adapted to an arbitrary structure depending on the problem at hand. Our approach is not limited to scalar-valued images and can also be used for vector-valued (multichannel) images such as gradient vector flow fields. We present realizations of a scalar-valued and a vector-valued multichannel filter. Our proposed algorithm was quantitatively evaluated on colorectal cancer cell lines (cells grown under controlled conditions), on which we successfully detected complex 3D mitotic structures. For a qualitative evaluation we tested our algorithms on human 3D tissue samples of colorectal cancer. We compare our results with a steerable filter approach as well as a morphology-based approach.

In this paper, we present a novel approach for identifying objects using touch sensors installed in the finger tips of a manipulation robot. Our approach operates on low-resolution intensity images that are obtained when the robot grasps an object. We apply a bag-of-words approach for object identification. By means of unsupervised clustering on training data, our approach learns a vocabulary from tactile observations which is used to generate a histogram codebook. The histogram codebook models distributions over the vocabulary and is the core identification mechanism. As the objects are larger than the sensor, the robot typically needs multiple grasp actions at different positions to uniquely identify an object. To reduce the number of required grasp actions, we apply a decision-theoretic framework that minimizes the entropy of the probabilistic belief about the type of the object. In our experiments carried out with various industrial and household objects, we demonstrate that our approach is able to discriminate between a large set of objects. We furthermore show that using our approach, a robot is able to distinguish visually similar objects that have different elasticity properties by using only the information from the touch sensor.

It is well known that linear filters are not powerful enough for many low-level image processing tasks. However, it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are, at the same time, equivariant with respect to translation and rotation. This paper proposes a new class of rotation-equivariant nonlinear filters that is based on the principle of group integration. These filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results. The relations of the proposed approach to Volterra filters and steerable filters are shown. In the context of detection problems, the filter may be interpreted as some kind of generalized Hough transform. The experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images. In the detection context, our experiments show that the proposed filter is definitely superior to alternative approaches, when high localization accuracy is required.

Steerable filters are a valuable tool for various low-level vision tasks. In this paper, we argue for the use of complex analysis in the context of 2-D steerable filters. In particular, we recommend the use of complex partial derivatives as a computational basis. Complex derivatives have a major advantage in comparison to real derivatives: they show a canonical rotation behavior, namely a rotation affects the derivative just by a multiplication with a complex unit number. So, the complex derivatives can be steered in a more elegant way and above that they are less expensive to compute. We present several analytical formulas for common and new filter kernels in terms of complex derivatives. Further we relate the complex derivatives of a Gaussian with the Gauss-Laguerre transform and show that the Gauss-Laguerre functions provide an optimal signal representation for local and smooth images. We discuss various finite difference schemes for the realization of the derivatives and use them in practice. In a first experiment, we use a newly introduced filter kernel for anisotropic blurring. The complex formalism offers an elegant way to locally adapt the shape and orientation of the kernel. Second, we use the proposed filters as matched filters to detect vessels in retinal images.