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Traditional stereo algorithms either explicitly use the frontal parallel plane assumption by only considering position (zero-order) disparity when computing similarity measures of two image windows, or implicitly use it by imposing a smoothness prior bias towards frontal parallel plane solution. However this introduces two types of systematic error for slanted or curved surfaces. The first type is structural, and relates to discrete pixel coordinates and neighborhood structure. The second is geometric, and relates to differential properties of surfaces. To eliminate these systematic errors we extend stereo matching to include first-order disparities. Contextual information is then expressed geometrically by transporting surface normals over overlapping neighborhoods, which takes a particularly simple (and efficient) form in the tangent plane approximation. In particular, we develop a novel stereo algorithm that combines first-order disparity information with position (zero-order) disparity for slanted surfaces, and illustrate its use.

Stereo for Slanted Surfaces: First Order Disparities and Normal Consistency