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Methods to quantify trabecular orientation are crucial in order to assess the exact trajectory of trabeculae in anatomical and histological sections. Specific methods for evaluating trabecular orientation include the ‘point counting’ technique (Whitehouse, 1974), manual tracing of trabecular outlines on a digitising board (Whitehouse, 1980), textural analysis (Veenland et al. 1998), graphic representation of vectors (Shimizu et al. 1993; Kamibayashi et al. 1995) and both mathematical (Geraets, 1998) and fractal analysis (Millard et al. 1998). Optical and computer‐assisted methods to detect trabecular orientation of bone using the Fourier transform were introduced by Oxnard (1982) later refined by Kuo & Carter (1991) (see also Oxnard, 1993, for a review), in the analysis of planar sections of vertebral bodies as well as in planar radiographs of cancellous bone in the distal radius (Wigderowitz et al. 1997). At present no studies have applied this technique to 2‐D images or to the study of dried bones. We report a universal computer‐automated technique for assessing the preferential orientation of the tibial subarticular trabeculae based on Fourier analysis, emphasis being placed on the search for improvements in accuracy over previous methods and applied to large stereoscopic (2‐D) fields of anatomical sections of dried human tibiae. Previous studies on the trajectorial architecture of the tibial epiphysis (Takechi, 1977; Maquet, 1984) and research data about trabecular orientation (Kamibayashi et al. 1995) have not employed Fourier analysis.

An analogue method, based on the concept of the achromatic diffraction process, is proposed for assessing the dependence of the colour structure of a two-dimensional image on its spatial frequencies by using conventional spatial filters. Some aspects of the description of a colour pupil in terms of diffraction are discussed. Experimental results are also presented and demonstrate the ability of the system to provide an experimental basis for the development of a system of spatial and colorimetric vision.

We show how contrast (C) affects the recognition of defocused letters. To do this, the maximum distance (threshold distance) at which a subject, with an induced refraction of −5.5 D, can recognize a letter was determined. Our results show that whenC = 1, the recognition threshold distance is such that the ratioη/ξ between the pseudoimage of the letter (η) and the blur circle (ζ), corresponding to any point of the letter at this distance is aboutη/ξ= 2; the exact value depends on the difficulty of recognition, in agreement with previous experiments. This ratio represents the sharpness of the image in a geometrical treatment of image formation, providing a geometrical criterion for recognition. Reduction in contrast can be compensated by improving the geometrical sharpness; i.e. bringing the object closer to the subject's are point. Our results show that the increment ofη/ξ as a function of the contrast is betweenC = 0.1and1.0. We suggest that a similar geometrical criterion for recognition could be used for any contrast (at least down toC = 0.1 and defocus > 1 D), provided that the proper value ofηξ is used in each case. On this basis we propose a purely geometrical model, which agrees well with the data and predicts the relationships between tolerance to defocus, contrast and visual acuity; including the well-known relation between visual acuity and defocus when contrast is unity.