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We address several shortcomings of the widely used gradient magnitude-based edge strength model through the computation of a hypothetical Human Visual System (HVS) response at edge locations. Contrary to gradient magnitude, the resulting \u201cvisual significance\u201d values account for various HVS mechanisms such as luminance adaptation and visual masking, and are scaled in perceptually linear units that are uniform across images. The visual significance computation is implemented in a fast multiscale second-generation wavelet framework which we use to demonstrate the differences in image retargeting, HDR image stitching, and tone mapping applications with respect to the gradient magnitude model. 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