Detecting soft shadows in a single outdoor image: From local edge-based models to global constraints

• An edge-based local model of the boundary and intensity of a soft shadow.
• A global constraint on the smoothness of the soft shadow width.
• A novel method for localizing the hard and soft edges of soft shadows in a single image.
• A unified framework for detecting both the penumbra and umbra in outdoor scenes.

Detecting soft shadows from a single image has been a difficult problem because soft shadows usually retain the textures of their backgrounds and because pixel intensities are greatly variable. In this paper, we propose a novel approach to automatically detect soft shadow edges from a single outdoor photograph. We first propose an edge-based model of a soft shadow boundary and parameterize three features. Then, motivated by the observation that the intensity profiles along the normal direction of the hard shadow edge can be approximated by a Sigmoid function, we develop an intensity model including the intensity, intensity change rate and intensity variance of the soft shadow. By fitting the intensity model of the soft shadows, three features of the boundary model are obtained and the initial segments of the soft shadow boundary are localized. Finally, to generate a continuous boundary, a level set-based optimization process is utilized with a global constraint on shadow width. Experiments demonstrate the effectiveness and flexibility of our method.

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