Estimating maps among large collections of objects (e.g., dense correspondences across images and 3D shapes) is a fundamental problem across a wide range of domains. In this paper, we provide theoretical justifications of spectral techniques for the map synchronization problem, i.e., it takes as input a collection of objects and noisy maps estimated between pairs of objects along a connected ob...

Let M be a complete metric ANR-space such that for any metric compactum K the function space C(K,M) contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that M has the following property: If f : X → Y is a perfect surjection between metric spaces, then C(X,M) with the source limitation topology contains a dense Gδ-subset of maps g such that all restrictions g|f(y), y ∈ Y , are ...

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topolo...

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topolo...

This paper addresses the problem of segmenting dense range data containing curved surfaces. Segmentation is a crucial step in the processing of range data for applications in object recognition, measurement, reengineering and modeling. We propose a two stage process using model-based curvature classification as an initial grouping. Features based on differential geometry, mainly curvature featu...

We address the problem of automating the processing of dense range data, specifically the automated interpretation of such data containing curved surfaces. This is a crucial step in the automated processing of range data for applications in object recognition, measurement, re-engineering and modeling. We propose a two stage process using model-based curvature classification as the first step. F...