Regularities like symmetry (mirror reflection) and repetition (translation) play an important role in both visual and haptic (active touch) shape perception. Altering figure-ground factors to change what is perceived as an object influences regularity detection. For vision, symmetry is usually easier to detect within one object, whereas repetition is easier to detect across two objects. For haptics, we have not found this interaction between regularity type and objectness (Cecchetto & Lawson, Journal of Experimental Psychology: Human Perception and Performance, 43, 103–125, 2017; Lawson, Ajvani, & Cecchetto, Experimental Psychology, 63, 197–214, 2016). However, our studies used repetition stimuli with mismatched concavities, convexities, and luminance, and so had mismatched contour polarities. Such stimuli may be processed differently to stimuli with matching contour polarities. We investigated this possibility. For haptics, speeded symmetry and repetition detection for novel, planar shapes was similar. Performance deteriorated strikingly if contour polarity mismatched (keeping objectness constant), whilst there was a modest disadvantage for between-2objects:facing-sides compared to within-1object:outer-sides comparisons (keeping contour polarity constant). For the same task for vision, symmetry detection was similar to haptics (strong costs for mismatched contour polarity, weaker costs for between-2objects:facing-sides comparisons), but repetition detection was very different (weak costs for mismatched contour polarity, strong benefits for between-2objects:facing-sides comparisons). Thus, objectness was less influential than contour polarity for both haptic and visual symmetry detection, and for haptic repetition detection. However, for visual repetition detection, objectness effects reversed direction (within-1object:outer-sides comparisons were harder) and were stronger than contour polarity effects. This pattern of results suggests that regularity detection reflects information extraction as well as regularity distributions in the physical world.