Three independent analysis methods were developed to investigate the distribution of solid mass in foams analyzed by X-ray tomography with effective pixel sizes larger than the thickness of the solid network (sub-pixel conditions). Validation of the methods was achieved by a comparison with the results obtained employing high-resolution tomography for the same set of foams. The foams showed different solid mass distribution, which varied from being preferentially located on the edges, with a fraction of mass in the struts nearing 0.6, to materials in which the fraction of mass in the struts was low, under 0.15. In all cases, the accuracy of the proposed approaches was greater for materials with a higher fraction of mass in the struts. The method based on deconvolution of the attenuation probability density function yielded the closest results to the high-resolution characterizations. In contrast, analysis of the solid matrix thickness distribution after watershed segmentation, and binarization of high thickness regions (struts segmentation) required normalization through macroscopic measurements and revealed higher deviations with respect to the high-resolution results. However, segmentation-based methods allowed investigation of the heterogeneity of the fraction of mass in the struts along the sample.

We apply common image enhancement principles and sub-pixel sample positioning to achieve a significant enhancement in the spatial resolution of a vertical scanning interferometer. We illustrate the potential of this new method using a standard atomic force microscope calibration grid and other materials having motifs of known lateral and vertical dimensions. This approach combines the high vertical resolution of vertical scanning interferometry and its native advantages (large field of view, rapid and nondestructive data acquisition) with important increases in lateral resolution. This combination offers the means to address a common challenge in microscopy: the integration of properties and processes that depend on, and vary as a function of observational length.

In the high-level operations of computer vision it is taken for granted that image features have been reliably detected. This paper addresses the problem of feature extraction by scale-space methods. There has been a strong development in scale-space theory and its applications to low-level vision in the last couple of years. Scale-space theory for continuous signals is on a firm theoretical basis. However, discrete scale-space theory is known to be quite tricky, particularly for low levels of scale-space smoothing. The paper is based on two key ideas: to investigate the stochastic properties of scale-space representations and to investigate the interplay between discrete and continuous images. These investigations are then used to predict the stochastic properties of sub-pixel feature detectors.

The modeling of image acquisition, image interpolation and scale-space smoothing is discussed, with particular emphasis on the influence of random errors and the interplay between the discrete and continuous representations. In doing so, new results are given on the stochastic properties of discrete and continuous random fields. A new discrete scale-space theory is also developed. In practice this approach differs little from the traditional approach at coarser scales, but the new formulation is better suited for the stochastic analysis of sub-pixel feature detectors.

The interpolated images can then be analysed independently of the position and spacing of the underlying discretisation grid. This leads to simpler analysis of sub-pixel feature detectors. The analysis is illustrated for edge detection and correlation. The stochastic model is validated both by simulations and by the analysis of real images.