Evidence from summation near threshold psychophysical experiments using compound Glass patterns is presented which supports the existence of mechanisms in the human visual system tuned for coherence in radial and concentric, and +45 degrees and -45 degrees spiral orientations. It is suggested that sensitivity to +45 degrees and -45 degrees logarithmic spirals serves to disambiguate the sense of spiral form, which would not be uniquely specified by measures of the components of orientation along the radial and concentric directions alone. A spiral space is introduced within which radial and concentric patterns are diametrically opposed on one axis and spirals of +45 degrees and -45 degrees on an orthogonal axis and it is proposed that these represent cardinal axes for detecting global structure. Comparison of the sensitivity tuning functions of the four mechanisms tuned to these axes with sensitivity to simple spiral Glass patterns shows that weighted combinations of output from adjacent pairs of this set of mechanisms are sufficient to account for absolute sensitivity to logarithmic spiral Glass patterns of all intermediate spiral angles. Control experiments demonstrate that the combinations are labeled for spiral sense (simple spirals of -22.5 degrees spiral angle can be discriminated from +22.5 degrees spirals at threshold for detection) and that adaptation transfers across quadrants of spiral space (adaptation to spirals of -22.5 degrees results in a decrease in sensitivity to orthogonal +22.5 degrees and -67.5 degrees spirals). Together these observations suggest that sensitivity to spirals in each of the quadrants of spiral space is due to higher order mechanisms reliant on output from 0 degrees, 90 degrees, +45 degrees and -45 degrees cardinal mechanisms. Crown copyright (c) 2007 Published by Elsevier Ltd. All rights reserved.