We propose a new strategy to design recursive implementations of the Gaussian filter and Gaussian regularized derivative filters. Each recursive filter consists of a cascade of two stable N th -order subsystems (causal and anti-causal). The computational complexity is 2N multiplications per pixel per dimension independent of the size (σ) of the Gaussian kernel. The filter coefficients have a closed-form solution as a function of scale (σ) and recursion order N (N=3,4,5). The recursive filters yield a high accuracy and excellent isotropy in n-D space.

The programmable array microscope (PAM) uses a spatial light modulator (SLM) to generate an arbitrary pattern of conjugate illumination and detection elements. The SLM dissects the fluorescent light imaged by the objective into a focal conjugate image, I c , formed by the 'in-focus' light, and a nonconjugate image, I nc , formed by the 'out-of-focus' light. We discuss two different schemes for confocal imaging using the PAM. In the first, a grid of points is shifted to scan the complete image. The second, faster approach, uses a short tiled pseudorandom sequence of two-dimensional patterns. In the first case, I c is analogous to a confocal image and I nc to a conventional image minus I c . In the second case I c and I nc are the sum and the difference, respectively, of a conventional and a confocal image. The pseudorandom sequence approach requires post-processing to retrieve the confocal part, but generates significantly higher signal levels for an equivalent integration time.

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In this paper we develop four measures to describe the distribution of nuclear chromatin. These measures attempt to describe in an objective and meaningful way the heterogeneity, granularity, condensation, and margination of chromatin in cell nuclei. Starting with a high-resolution digitized image of a cell where the nuclear pixels have been identified, the four measures may be rapidly estimated. The range of each is derived and the interpretation of the measures in the context of chromatin compaction and distribution is developed. Implementation issues such as sampling density, thresholding and subsequent pre-processing, and algorithmic complexity are discussed.Key terms: Quantitative microscopy, image processing, texture measures, pattern recognition, image measurementIn this paper we present four measures that we have developed to quantify and characterize the distribution of chromatin in the nuclei of stained cells. These measures are based upon a simple model for the way chromatin compacts in a cell nucleus and how that compaction is reflected in verbal descriptions of nuclear "texture." Use of the word texture immediately sug gests a range of possibilities for quantification and it is not our purpose here to go into a lengthy review of the texture literature. What has guided us in this study, however, has been a search for ways of describing chromatin distribution that clearly relate to the underlying processes that cause change in the appearance of cell nuclei. Thus we start from a somewhat different perspective then the mathematical texture parameters of Haralick (5), Galloway (3, or Pressman (16). METHODS ModelingWe begin with the idea that a cell nucleus (as pictured in Figs. 1A,B) has a constant amount of DNA except when the cell is synthesizing DNA or about to divide.Thus we are considering cells with a normal, diploid (212) DNA content-GO and G1 cells. In a typical cell population such cells will account for at least 85% of all randomly sampled cells (14). It is precisely these cells that we are interested in characterising with respect to chromatin distribution; cells with a DNA complement above the 2c level are easily found by measuring their DNA content. If a difference exists between the nuclear chromatin pattern in two similar cells, then, according to our model of constant DNA, it must be due to a redistribution of the chromatin within the nucleus. This is illustrated in Figure 2A-D where all four cell images have precisely the same total nuclear optical density (proportional to DNA) but the distributions have been artificially altered.We describe the possible chromatin variations in terms of three linguistic attributes: heterogeneity, granularity, and margination. The first, heterogeneity, refers to whether the nuclear chromatin is homogeneously distributed throughout the nucleus or condensed into granules.If the chromatin is condensed, then the description of granularity assumes a useful role. While Figures 2C and D both exhibit an artificial granularity, the size of the "granules" differs s...

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