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Range image registration and surface reconstruction have been traditionally considered as two independent problems where the latter relies on the results of the former. This paper presents a new approach to surface recovery from range images where these two processes are integrated and performed in a common volumetric representation. The volumetric representation contains both implicitly represented reconstructed surface as the signed distance field and corresponding matching information in the form of the gradient of the distance field. This allows both simultaneous and incremental registration where matching complexity is linear with respect to the number of images. This improvement leads to incremental modeling from range image acquisition to surface reconstruction. It is shown that the approach is tolerant to initial registration errors as well as to measurement errors while keeping the details of the initial range images. The paper describes the formalism of the approach. Experimental results demonstrate performance advantages, tolerance to aforementioned types of errors and, as an application, filtering using redundant range data without loss of sharp details on the reconstructed surface.