Many parameters have been investigated as to their effect on the way in which the visual system is able to integrate different motion directions at the same visual location. Of special interest have been parameters that determine the depth relationship between surfaces, such as disparity, relative contrast, and occlusion versus transparency. The preferred stimulus for this research has been the 'plaid', usually constructed from two linear gratings. The present study concentrated not on these Cartesian plaids, but on polar plaids, made from a combination of concentric circles and radial gratings. These kinds of plaids also have a special theoretical significance: within the Lie Transformation Group approach to visual pattern processing, Cartesian and polar stimuli represent different invariances in the visual world. This study compared Cartesian, polar and hybrid plaids as to their propensity to be perceived as coherently moving stimuli. Cartesian and polar plaids were similar in terms of the effects of intersection luminance and relative contrast on coherence, polar plaids being consistently less coherent. Hybrid plaids did not usually cohere at all. Adaptation to an unambiguously coherent plaid decreased perceived coherence when tested with a bistable plaid from the same, and not from the other Lie group, i.e. there was within-group adaptation but no between-group adaptation. Polar plaids also offer the possibility of studying the influence of another depth parameter on motion integration: expansion or contraction of circular gratings, which represent motion-in-depth toward or away from the observer. This motion-in-depth was tested for interaction with disparity or relative contrast in the determination of motion integration. The results were negative under the present conditions. Thus not all depth parameters contribute equally to the determination of the stimulus depth relations affecting the motion integration process.