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This report describes a fourth order tensor defined on projective spaces which can be used for the representation of medium-level features, e.g., one or more oriented segments. The tensor has one part which describes what type of local structures are present in a region, and one part which describes where they are located. This information can be used, e.g., to represent multiple orientations, corners, and line-endings. The tensor can be defined for arbitrary signal dimension, but the presentation focuses on the properties of the fourth order tensor for the case of 2D and 3D image data. A method for estimating the proposed tensor representation by means of simple computations directly from the structure tensor is presented. Given a simple matrix representation of the tensor, it can be shown that there is a direct correspondence between the number of oriented segments and the rank of the matrix provided that the number of segments is three or less. The \publication also presents techniques for extracting information about the oriented segments which the tensor represent. Finally, it shown that a small set of coefficients can be computed from the proposed tensor which are invariant to changes of the coordinate system
Historic Preservation Act of 1966: Past, Present, Future
The Historic Preservation Act of 1966 has significantly impacted communities at local, regional, state and national levels. However, questions have been raised about historic preservation and its contribution to economic development. The intersection of sustainability issues such as adaptive reuse, air quality, “walkable-livable” neighborhoods, and fossil fuel consumption illustrate the increasing importance of historic preservation. Historic Preservation Tax Credits show high returns and are valuable tools for legislators and policy makers to utilize in collaboration with other community development programs. Research indicates that historic preservation can be utilized as a tool to elevate property values, restore pedestrian-friendly neighborhoods, maintain community health, promote creative entrepreneurship and implement long-term sustainability efforts. Grand Rapids, Michigan provides a case study for assessment. The State of Michigan may benefit in the future from extension of historic preservation tax credits on a state-wide level
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