For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every number between one and the number of data, the result is a function, the cluster structure function. It maps the number of parts of a partition to values related to the deficiencies of being good models by the parts. Such a function starts with a value at least zero for no partition of the data set and descents to zero for the partition of the data set into singleton parts. The optimal clustering is the one selected by analyzing the cluster structure function. The theory behind the method is expressed in algorithmic information theory (Kolmogorov complexity). In practice the Kolmogorov complexities involved are approximated by a concrete compressor. We give examples using real data sets: the MNIST handwritten digits and the segmentation of real cells as used in stem cell research.

Biomineralization is the process by which organisms use minerals to harden their tissues and provide them with physical support. Biomineralizing cells concentrate the mineral in vesicles that they secret into a dedicated compartment where crystallization occurs. The dynamics of vesicle motion and the molecular mechanisms that control it, are not well understood. Sea urchin larval skeletogenesis provides an excellent platform for investigating the kinetics of mineral-bearing vesicles. Here we used lattice light-sheet microscopy to study the three-dimensional (3D) dynamics of calcium-bearing vesicles in the cells of normal sea urchin embryos and of embryos where skeletogenesis is blocked through the inhibition of Vascular Endothelial Growth Factor Receptor (VEGFR). We developed computational tools for displaying 3D-volumetric movies and for automatically quantifying vesicle dynamics. Our findings imply that calcium vesicles perform an active diffusion motion in both, calcifying (skeletogenic) and non-calcifying (ectodermal) cells of the embryo. The diffusion coefficient and vesicle speed are larger in the mesenchymal skeletogenic cells compared to the epithelial ectodermal cells. These differences are possibly due to the distinct mechanical properties of the two tissues, demonstrated by the enhanced f-actin accumulation and myosinII activity in the ectodermal cells compared to the skeletogenic cells. Vesicle motion is not directed toward the biomineralization compartment, but the vesicles slow down when they approach it, and probably bind for mineral deposition. VEGFR inhibition leads to an increase of vesicle volume but hardly changes vesicle kinetics and doesn't affect f-actin accumulation and myosinII activity. Thus, calcium vesicles perform an active diffusion motion in the cells of the sea urchin embryo, with diffusion length and speed that inversely correlate with the strength of the actomyosin network. Overall, our studies provide an unprecedented view of calcium vesicle 3D-dynamics and point toward cytoskeleton remodeling as an important effector of the motion of mineral-bearing vesicles.

SUMMARY: Light microscopes can now capture data in five dimensions at very high frame rates producing terabytes of data per experiment. Five-dimensional data has three spatial dimensions (x, y, z), multiple channels (λ) and time (t). Current tools are prohibitively time consuming and do not efficiently utilize available hardware. The hydra image processor (HIP) is a new library providing hardware-accelerated image processing accessible from interpreted languages including MATLAB and Python. HIP automatically distributes data/computation across system and video RAM allowing hardware-accelerated processing of arbitrarily large images. HIP also partitions compute tasks optimally across multiple GPUs. HIP includes a new kernel renormalization reducing boundary effects associated with widely used padding approaches. AVAILABILITY AND IMPLEMENTATION: HIP is free and open source software released under the BSD 3-Clause License. Source code and compiled binary files will be maintained on http://www.hydraimageprocessor.com. A comprehensive description of all MATLAB and Python interfaces and user documents are provided. HIP includes GPU-accelerated support for most common image processing operations in 2-D and 3-D and is easily extensible. HIP uses the NVIDIA CUDA interface to access the GPU. CUDA is well supported on Windows and Linux with macOS support in the future.

One of the most important and error-prone tasks in biological image analysis is the segmentation of touching or overlapping cells. Particularly for optical microscopy, including transmitted light and confocal fluorescence microscopy, there is often no consistent discriminative information to separate cells that touch or overlap. It is desired to partition touching foreground pixels into cells using the binary threshold image information only, and optionally incorporating gradient information. The most common approaches for segmenting touching and overlapping cells in these scenarios are based on the watershed transform. We describe a new approach called pixel replication for the task of segmenting elliptical objects that touch or overlap. Pixel replication uses the image Euclidean distance transform in combination with Gaussian mixture models to better exploit practically effective optimization for delineating objects with elliptical decision boundaries. Pixel replication improves significantly on commonly used methods based on watershed transforms, or based on fitting Gaussian mixtures directly to the thresholded image data. Pixel replication works equivalently on both 2-D and 3-D image data, and naturally combines information from multi-channel images. The accuracy of the proposed technique is measured using both the segmentation accuracy on simulated ellipse data and the tracking accuracy on validated stem cell tracking results extracted from hundreds of live-cell microscopy image sequences. Pixel replication is shown to be significantly more accurate compared with other approaches. Variance relationships are derived, allowing a more practically effective Gaussian mixture model to extract cell boundaries for data generated from the threshold image using the uniform elliptical distribution and from the distance transform image using the triangular elliptical distribution.

The analysis of time-lapse images showing cells dividing to produce clones of related cells is an important application in biological microscopy. Imaging at the temporal resolution required to establish accurate tracking for vertebrate stem or cancer cells often requires the use of transmitted light or phase-contrast microscopy. Processing these images requires automated segmentation, tracking and lineaging algorithms. There is also a need for any errors in the automated processing to be easily identified and quickly corrected. We have developed LEVER, an open source software tool that combines the automated image analysis for phase-contrast microscopy movies with an easy-to-use interface for validating the results and correcting any errors. AVAILABILITY AND IMPLEMENTATION: LEVER is available free and open source, licensed under the GNU GPLv3. Details on obtaining and using LEVER are available at http://n2t.net/ark:/87918/d9rp4t CONTACT: [email protected].

Pairwise normalized compression distance (NCD) is a parameter-free, feature-free, alignment-free, similarity metric based on compression. We propose an NCD of multisets that is also metric. Previously, attempts to obtain such an NCD failed. For classification purposes it is superior to the pairwise NCD in accuracy and implementation complexity. We cover the entire trajectory from theoretical underpinning to feasible practice. It is applied to biological (stem cell, organelle transport) and OCR classification questions that were earlier treated with the pairwise NCD. With the new method we achieved significantly better results. The theoretic foundation is Kolmogorov complexity.

BACKGROUND: Neural stem cells are motile and proliferative cells that undergo mitosis, dividing to produce daughter cells and ultimately generating differentiated neurons and glia. Understanding the mechanisms controlling neural stem cell proliferation and differentiation will play a key role in the emerging fields of regenerative medicine and cancer therapeutics. Stem cell studies in vitro from 2-D image data are well established. Visualizing and analyzing large three dimensional images of intact tissue is a challenging task. It becomes more difficult as the dimensionality of the image data increases to include time and additional fluorescence channels. There is a pressing need for 5-D image analysis and visualization tools to study cellular dynamics in the intact niche and to quantify the role that environmental factors play in determining cell fate. RESULTS: We present an application that integrates visualization and quantitative analysis of 5-D (x,y,z,t,channel) and large montage confocal fluorescence microscopy images. The image sequences show stem cells together with blood vessels, enabling quantification of the dynamic behaviors of stem cells in relation to their vascular niche, with applications in developmental and cancer biology. Our application automatically segments, tracks, and lineages the image sequence data and then allows the user to view and edit the results of automated algorithms in a stereoscopic 3-D window while simultaneously viewing the stem cell lineage tree in a 2-D window. Using the GPU to store and render the image sequence data enables a hybrid computational approach. An inference-based approach utilizing user-provided edits to automatically correct related mistakes executes interactively on the system CPU while the GPU handles 3-D visualization tasks. CONCLUSIONS: By exploiting commodity computer gaming hardware, we have developed an application that can be run in the laboratory to facilitate rapid iteration through biological experiments. We combine unsupervised image analysis algorithms with an interactive visualization of the results. Our validation interface allows for each data set to be corrected to 100% accuracy, ensuring that downstream data analysis is accurate and verifiable. Our tool is the first to combine all of these aspects, leveraging the synergies obtained by utilizing validation information from stereo visualization to improve the low level image processing tasks.

An algorithmic information-theoretic method is presented for object-level summarization of meaningful changes in image sequences. Object extraction and tracking data are represented as an attributed tracking graph (ATG). Time courses of object states are compared using an adaptive information distance measure, aided by a closed-form multidimensional quantization. The notion of meaningful summarization is captured by using the gap statistic to estimate the randomness deficiency from algorithmic statistics. The summary is the clustering result and feature subset that maximize the gap statistic. This approach was validated on four bioimaging applications: 1) It was applied to a synthetic data set containing two populations of cells differing in the rate of growth, for which it correctly identified the two populations and the single feature out of 23 that separated them; 2) it was applied to 59 movies of three types of neuroprosthetic devices being inserted in the brain tissue at three speeds each, for which it correctly identified insertion speed as the primary factor affecting tissue strain; 3) when applied to movies of cultured neural progenitor cells, it correctly distinguished neurons from progenitors without requiring the use of a fixative stain; and 4) when analyzing intracellular molecular transport in cultured neurons undergoing axon specification, it automatically confirmed the role of kinesins in axon specification.