C.L. Luengo Hendriks

Integrating Data Clustering and Visualization for the Analysis of 3D Gene Expression Data

The recent development of methods for extracting precise measurements of spatial gene expression patterns from three-dimensional (3D) image data opens the way for new analyses of the complex gene regulatory networks controlling animal development. We present an integrated visualization and analysis framework that supports user-guided data clustering to aid exploration of these new complex data sets. The interplay of data visualization and clustering-based data classification leads to improved visualization and enables a more detailed analysis than previously possible. We discuss 1) the integration of data clustering and visualization into one framework, 2) the application of data clustering to 3D gene expression data, 3) the evaluation of the number of clusters k in the context of 3D gene expression clustering, and 4) the improvement of overall analysis quality via dedicated postprocessing of clustering results based on visualization. We discuss the use of this framework to objectively define spatial pattern boundaries and temporal profiles of genes and to analyze how mRNA patterns are controlled by their regulatory transcription factors.

Improving the accuracy of isotropic granulometries

Morphological sieves are capable of classifying objects in images according to their size. They yield a granulometry, which describes the imaged structure. The discrete sieve has some disadvantages that its continuous-domain counterpart does not have: sampled disks (used as isotropic structuring elements) are rather anisotropic, especially at small scales, and their area, as a function of the size in the continuous domain, shows jumps at apparently arbitrary locations. These problems cause a severe bias and low precision of the derived size distribution. Therefore we propose a new digitization scheme for implementing continuous sieves. First we increase the sampling density of the structuring element and the image. This does not add new detail to the image, but yields a sampled structuring element that is a much better approximation to its continuous counterpart, and thereby substantially reduces the discretization error. The second innovation is to shift the structuring element with respect to the sampling grid; this makes the size increments smoother, and further reduces the discretization errors. These ideas are validated on synthetic images. We also show that the proposed improvements allow for a finer scale sampling.

Discrete Morphology with Line Structuring Elements

Discrete morphological operations with line segments are notoriously hard to implement. In this paper we study different possible implementations of the line structuring element, compare them, and examine their rotation and translation invariance in the continuous domain. That is, we are interested in obtaining a morphological operator that is invariant to rotations and translations of the image before sampling.

Using line segments as structuring elements for sampling-invariant measurements

When performing measurements in digitized images, the pixel pitch does not necessarily limit the attainable accuracy. Proper sampling of a bandlimited continuous-domain image preserves all information present in the image prior to digitization. It is therefore (theoretically) possible to obtain measurements from the digitized image that are identical to measurements made in the continuous domain. Such measurements are sampling invariant, since they are independent of the chosen sampling grid. It is impossible to attain strict sampling invariance for filters in mathematical morphology due to their nonlinearity, but it is possible to approximate sampling invariance with arbitrary accuracy at the expense of additional computational cost. In this paper, we study morphological filters with line segments as structuring elements. We present a comparison of three known and three new methods to implement these filters. The method that yields a good compromise between accuracy and computational cost employs a (subpixel) skew to the image, followed by filtering along the grid axes using a discrete line segment, followed by an inverse skew. The staircase approximations to line segments under random orientations can be modeled by skewing a horizontal or vertical line segment. Rather than skewing the binary line segment we skew the image data, which substantially reduces quantization error. We proceed to determine the optimal number of orientations to use when measuring the length of line segments with unknown orientation.

Registering Drosophila embryos at cellular resolution to build a quantitative 3D atlas of gene expression patterns and morphology

The Berkeley Drosophila Transcription Network Project is developing a suite of methods to convert volumetric data generated by confocal fluorescence microscopy into numerical three dimensional representations of gene expression at cellular resolution. One key difficulty is that fluorescence microscopy can only capture expression levels for a few gene products in a given animal. We report on a method for registering 3D expression data from different Drosophila embryos stained for overlapping subsets of gene products in order to build a composite atlas, ultimately containing co-expression information for thousands of genes. Our techniques have also allowed the discovery of a complex pattern of cell density across the blastula that changes over time and may play a role in gastrulation.

The Generalised Radon Transform: Sampling and Memory Considerations

The generalised Radon transform is a well-known tool for detecting parameterised shapes in an image. Applying the Radon transform to an image results in a parameter response function (PRF). Curves in the image become peaks in the PRF. The location of a peak corresponds to the parameters of a shape, and the amplitude to the amount of evidence for that shape. In this paper we discuss two important aspects of the Radon transform. The first aspect is discretisation. Using concepts from sampling theory we derive a set of sampling criteria for the Radon transform. The second aspect concerns a projection-based algorithm to reduce memory requirements.