Summary It is generally accepted that the functional compartmentalization of eukaryotic cells is reflected by the differential occurrence of proteins in their compartments. The location and physiological function of a protein are closely related; local information of a protein is thus crucial to understanding its role in biological processes. The visualization of proteins residing on intracellular structures by fluorescence microscopy has become a routine approach in cell biology and is increasingly used to assess their colocalization with well-characterized markers. However, imageanalysis methods for colocalization studies are a field of contention and enigma. We have therefore undertaken to review the most currently used colocalization analysis methods, introducing the basic optical concepts important for image acquisition and subsequent analysis. We provide a summary of practical tips for image acquisition and treatment that should precede proper colocalization analysis. Furthermore, we discuss the application and feasibility of colocalization tools for various biological colocalization situations and discuss their respective strengths and weaknesses. We have created a novel toolbox for subcellular colocalization analysis under Image J, named JACoP, that integrates current global statistic methods and a novel object-based approach.

A guided tour into subcellular colocalization analysis in light microscopy

The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate differences between watershed transforms based on different definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.

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The watershed transform: definitions, algorithms and parallelization strategies

Digital inpainting provides a means for reconstruction of small damaged portions of an image. Although the inpainting basics are straightforward, most inpainting techniques published in the literature are complex to understand and implement. We present here a new algorithm for digital inpainting based on the fast marching method for level set applications. Our algorithm is very simple to implement, fast, and produces nearly identical results to more complex, and usually slower, known methods. Source code is available online.

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An Image Inpainting Technique Based on the Fast Marching Method

The watershed transform has interesting properties that make it useful for many different image segmentation applications: it is simple and intuitive, can be parallelized, and always produces a complete division of the image. However, when applied to medical image analysis, it has important drawbacks (oversegmentation, sensitivity to noise, poor detection of thin or low signal to noise ratio structures). We present an improvement to the watershed transform that enables the introduction of prior information in its calculation. We propose to introduce this information via the use of a previous probability calculation. Furthermore, we introduce a method to combine the watershed transform and atlas registration, through the use of markers. We have applied our new algorithm to two challenging applications: knee cartilage and gray matter/white matter segmentation in MR images. Numerical validation of the results is provided, demonstrating the strength of the algorithm for medical image segmentation.

Improved watershed transform for medical image segmentation using prior information

Morphological attribute profiles (APs) are defined as a generalization of the recently proposed morphological profiles (MPs). APs provide a multilevel characterization of an image created by the sequential application of morphological attribute filters that can be used to model different kinds of the structural information. According to the type of the attributes considered in the morphological attribute transformation, different parametric features can be modeled. The generation of APs, thanks to an efficient implementation, strongly reduces the computational load required for the computation of conventional MPs. Moreover, the characterization of the image with different attributes leads to a more complete description of the scene and to a more accurate modeling of the spatial information than with the use of conventional morphological filters based on a predefined structuring element. Here, the features extracted by the proposed operators were used for the classification of two very high resolution panchromatic images acquired by Quickbird on the city of Trento, Italy. The experimental analysis proved the usefulness of APs in modeling the spatial information present in the images. The classification maps obtained by considering different APs result in a better description of the scene (both in terms of thematic and geometric accuracy) than those obtained with an MP.

Morphological Attribute Profiles for the Analysis of Very High Resolution Images

A new general algorithm for computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the computation per row (column) is independent of the computation of other rows (columns), the algorithm can be easily parallelized on shared memory computers. The algorithm can be used for the computation of the exact Euclidean, Manhattan (L 1 norm), and chessboard distance (L ∞ norm) transforms.

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A general algorithm for computing distance transforms in linear time

The implementation of morphological connected set operators for image filtering and pattern recognition is discussed. Two earlier algorithms based on priority queues and hierarchical queues, respectively, are compared to a more recent union-find approach. Unlike the earlier algorithms which process regional extrema in the image sequentially, the union-find method allows simultaneous processing of extrema. In the context of area openings, closings, and pattern spectra, the union-find algorithm outperforms the previous methods on almost all natural and synthetic images tested. Finally, extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms, and memory usages are compared.

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A comparison of algorithms for connected set openings and closings

Morphological attribute filters have not previously been parallelized, mainly because they are both global and non-separable. We propose a parallel algorithm which achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings and thickenings, based on Salembier's Max-Trees and Min-trees. The image or volume is first partitioned in multiple slices. We then compute the Max-trees of each slice using any sequential Max-Tree algorithm. Subsequently, the Max-trees of the slices can be merged to obtain the Max-tree of the image. A C-implementation yielded good speed-ups on both a 16-processor MIPS 14000 parallel machine, and a dual-core Opteron-based machine. It is shown that the speed-up of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72% on a single-core processor, due to reduced cache thrashing.

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Arnold Meijster

Papers

The watershed transform: definitions, algorithms and parallelization strategies

A general algorithm for computing distance transforms in linear time

A comparison of algorithms for connected set openings and closings

Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines

The Watershed Transform: Definitions, Algorithms and Parallelization Strategies