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We propose a weak security notion for visual secret sharing (VSS) schemes. Under such a weak security notion, VSS schemes are designed to be secure against attackers' eyesight, but are not unconditionally secure, in general. In this paper, we theoretically discuss the relation between unconditionally secure (US) and weakly secure (WS) VSS schemes and present two constructions of WS-VSS schemes for color images. We show that WS-VSS schemes can achieve clearer color reproduced images with a smaller pixel expansion compared to those using US-VSS schemes, while we clarify that the basis matrices in both types of VSS schemes for black-white binary images are the same. These results suggest that the proposed VSS schemes can be regarded as ramp (or nonperfect) VSS schemes for color secret images.