The use of a suitable perceptual model is necessary to minimize visual distortion in marked images, because minor modifications to the pixels can be perceptible since the pixels are either black or white. In this paper, a new perceptual model is proposed for binary images that is useful for data hiding applications. In our model, the distortion that occurs after flipping a pixel is estimated on the novel curvature-weighted distance difference (CWDD) measure between two contour segments. Through subjective tests the perceptual measure is validated and highly correlated with human perception.