Computer aided image segmentation and graph construction of nerve cells from 3D confocal microscopy scans

Exact knowledge about the morphology of neuronal cells is essential in neurobiology and in medicine. The main goal of these disciplines is to study the influence of morphology upon the physiology of the neuronal cells. Comparative studies on a high number of cells, would thus facilitate: i) the better understanding of cortical circuitry and the monitoring of spontaneous or experimentally-induced developmental or plastic changes (Durst et al., 1994; Withers et al., 1995; Winnington et al., 1996; Witte et al., 1996; Zito et al., 1999), ii) the investigation of the influence of dendritic geometry on the integrative properties of a neuron (de Schutter and Bower, 1994a; de Schutter and Bower, 1994b; Hill et al., 1994; Rapp et al., 1994), iii) for mapping the spatial relationships and distances between different tracts and neuropils (Galizia et al., 1999; Laissue et al., 1999; Rein et al., 1999), as well as iv) the study of the consequences of genetic defects and degenerative modifications. Thus an automated procedure for the neuronal reconstruction is needed, since the currently available computer-aided segmentation and tracing procedures still necessitate the manual drawing of an expert. Therefore the so obtained results are not objectively quantifiable. Due to the complex morphology of the neuronal cells, this is additionally a time consuming task. The goal of automatic 3D-reconstructions of neuronal cells is hard to achieve. Due to the large variety of existing neuronal cell types (Figure 1.2) and probe characteristics (differences in staining, mounting and scanning procedures) no general solution can be given. The current work focuses on the construction of a preliminary neuronal graph from confocal microscopy scans of intracellularly stained neurons. This facilitates a subsequent automatic three-dimensional high-resolution geometric reconstruction of the cell (Schmitt et al., 2001), which is needed for the precise geometrical measurement of the neurons (de Schutter and Bower, 1994b). The here developed neuronal graph construction algorithm relies on several pre-processing steps for noise reduction, a contrast robust boundary detection, segmentation and tracing. Therefore a system is established in this work which performs the complete processing starting from the original image until a neuronal graph is obtained. This is in contrast to currently available methodology, which either reports results about one of the pre-processing steps enumerated above, or performs a graph construction on already segmented data. The image processing steps implemented in the current system are thus: 1. Image denoising is needed due to the large amount of background noise present in confocal microscopy images, which arises due to the low light intensities reaching the detector and the relatively high thermic signal generated by the photo multiplier tube. Therefore the SNR of the captured images is low and often, the captured gray values of foreground objects lie in the same range as the gray values of the background noise. Thus a denoising procedure is needed which keeps small sized and low contrasted neuronal branches and eliminates speckle noise. Denoising is performed in the current work by means of the orthogonal wavelet shrinkage paradigm, first introduced by David Donoho (Donoho, 1995b; Donoho and Johnstone, 1995). The 3D extension of Donoho’s wavelet shrinkage, introduced here for the first time, gives rise to several variants. The performance of these variants is analyzed on several 3D confocal microscopy scans of neurons (Dima et al., 1999a). However, an objective evaluation of the outcomes of several denoising variants (generated by the application of different wavelet filters and shrinkage modalities) of the same initial image is very difficult, since there is no ”ground truth” noiseless image available for comparison. This work shows, that the usually employed quality measures, such as the mean squared error (MSE), the entropy or the density of nonzero wavelet coefficients are not giving meaningful rankings, which are comparable with human judgment. Therefore a new intercale wavelet coefficients’ correlation measure is introduced, which is related to the scene scanning mechanism of the human visual system. This intercale correlation measure is then combined with other simple measures to quantify more of the conditions imposed to a well denoised image. The rankings given by the obtained new composed measures (Dima et al., 1999b) are compared with human evaluation. It is shown, that any of these measures perform better than the simple ones and a winner measure is determined. 2. Boundary detection is not an easy task in the case of neuronal data, since branch sizes can vary in the range between μm and mm and do have large contrast variations due to the inhomogeneity of the dye inside the branches. The multiscale edge detection is performed employing Mallat’s efficient multiscale ”A Trous” algorithm (Mallat and Zhong, 1992) (based on the Translation Invariant Wavelet Transform TIWT). This algorithm is extended here to 3D. However, since it finds even the lowest contrasted edges, it detects also small background fluctuations and noise. Therefore an edge selection method is needed. The current work develops a new across-scales edge validation method (Dima et al., 2001b) which computes a confidence measure of edge points corresponding to object boundaries. This validation strongly enhances coherent edges which are present on neighboring scales and have similar gradient direction. Therefore coefficients corresponding to noisy edges can be suppressed almost blindly by thresholding those having low confidence values. 3. The segmentation is based on a new paradigm called ”Gradient Tracing” (Dima et al., 2002) which uses the cleaned edges from the previous step and the associated gradient directions to determine the inside of the foreground objects. Since edge detection finds edges of even the finest and lowest contrasted objects, and Gradient Tracing considers all available edge information, smallest and weakest neuronal signal is retrieved. This is in contrast to currently available segmentation techniques, which either are based on thresholding or start from initially set points and grow a region based on the assumption of low contrast variations (He et al., 2001; Beucher and Meyer, 1993; Ge and Fitzpatrick, 1996; Gagvani and Silver, 1997; Xu et al., 1998; Schirmacher et al., 1998; Kim and Gilies, 1998; Zhou and Toga, 1999) a premise, which is almost never given in recordings of neuronal tissue leading thus to the loss of significant data at regions of strong contrast decrease. Additionally, the ”Gradient Tracing” paradigm computes in the same step branch symmetry points which lie along the central branch axes and estimates the axial direction at these points. These points form a raw skeleton of the analyzed objects and are further used for the graph construction along the neuronal branches. 4. Feature extraction is computed also in a multiscalar fashion, basing on the efficient TIWT to implement second order differential operators. The wavelet filter needed for this operator is derived in this work. These operators are then employed for the detection of branching and bending points of the neuron (n.b. independently from the skeletonization, which is in contrast to currently available branching point detection methods (Cesar Jr. and Costa, 1998)) and for the detection of circular objects. It is shown here, that the direct application of multiscale differential operators as it is usually done in literature (Kitchen and Rosenfeld, 1982; Florack et al., 1994; Lindeberg, 1998; Zheng et al., 1999) to noisy biological data does not give meaningful results. Instead, combined with the segmentation by Gradient Tracing, a correct feature detection is obtained for the first time on 3D neuronal data. 5. Graph construction is finally implemented basing on all previous preprocessing results (i.e. cleaned edges, the raw skeleton and its associated axes, the extracted branching and bending points and not the least original gray value data). This novel graph construction method (Dima et al., 2003) uses thus the most available information, unlike any similar method has used before (He et al., 2001; Herzog et al., 1998; Schirmacher et al., 1998; Zhou and Toga, 1999). This allows it to be more tolerant to image artifacts such as background noise or boundary irregularities and therefore to capture much more details of the underlying structure. The whole system, starting from the original image until the final graph is obtained needs the setting of two thresholds, and two neighborhood parameters and is thus almost automatic, without demanding any online user interaction. The future aim is to use the preliminary neuronal graph obtained here for a model based surface reconstruction (Schießl et al., 2001). The reconstructed neuron can further be used for geometric measurements, such as the local extraction of volume, branch diameters and length, or branching statistics. These can thereafter be used for the construction of multi-compartment models to simulate the electrical properties of the neuron (de Schutter and Bower, 1994a) for the estimation of those physiological parameters which cannot easily be measured. The long term goal is the analysis of the relation between neuronal morphology and physiology. Even if the final goal of the here presented algorithms is the graph construction, the single modules, such as the segmentation or the feature extraction do have a general character, such that the algorithms can be used also on other kinds of data. For example, the symmetry points computed by the ”Gradient Tracing” proofed to be useful as inputs for several image processing tasks. They are employed in the current work as seeds for a newly introduced variation of the Seed-Fill algorithm. This modified Seed-Fill algorithm is able to blindly segment obj