MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

Computational geometry

A Hu moment invariant as a shape circularity measure

We propose a strategy to decompose a polygon, containing zero or more holes, into ``approximately convex'' pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignoreless significant artifacts such as wrinkles and surface texture a user specified tolerance determines allowable concavity. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant non-convex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of `increasingly convex' decompositions. Our algorithm computes an ACD of a simple polygon with n verticesand r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard or,if the polygon has no holes, takes O(nr2) time.

/pdf/approximate-convex-decomposition-of-polygons-4wgoo2jclu.pdf

Approximate convex decomposition of polygons

We propose a strategy to decompose a polygon, containing zero or more holes, into ''approximately convex'' pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignore less significant artifacts such as wrinkles and surface texture. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant non-convex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of 'increasingly convex' decompositions. A user specified tolerance determines the degree of concavity that will be allowed in the lowest level of the hierarchy. Our algorithm computes an ACD of a simple polygon with n vertices and r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard or, if the polygon has no holes, takes O(nr^2) time. Models and movies can be found on our web-pages at: http://parasol.tamu.edu/groups/amatogroup/.

The paper introduces a shape measure intended to describe the extent to which a closed polygon is rectilinear. Other than somewhat obvious measures of rectilinearity (e.g., the sum of the differences of each corner's angle from multiples of 90/spl deg/), there has been little work in deriving a measure that is straightforward to compute, is invariant under scale, rotation, and translation, and corresponds with the intuitive notion of rectilinear shapes. There are applications in a number of different areas of computer vision and photogrammetry. Rectilinear structures often correspond to human-made objects and are therefore justified as attentional cues for further processing. For instance, in aerial image processing and reconstruction, where building footprints are often rectilinear on the local ground plane, building structures, once recognized as rectilinear, can be matched to corresponding shapes in other views for stereo reconstruction. Perceptual grouping algorithms may seek to complete shapes based on the assumption that the object in question is rectilinear. Using the proposed measure, such systems can verity this assumption.

Rectilinearity measurements for polygons

Convexity estimators are commonly used in the analysis of shape. In this paper we define and evaluate a new easily computable measure of convexity for polygons. Let be an arbitrary polygon. If denotes the perimeter in the sense of metrics of the polygon obtained by the rotation of by angle with the origin as the center of the applied rotation, and if is the Euclidean perimeter of the minimal rectangle having the edges parallel to coordinate axes which includes such a rotated polygon , then we show that defined as can be used as an estimate for the convexity of .S everal desirable properties of are proved, as well.

/pdf/a-convexity-measurement-for-polygons-dsmjov9qd1.pdf

A Convexity Measurement for Polygons

In this paper we define a function R(P) which is defined for any polygon P and which maps a given polygon P into a number from the interval (0, 1]. The number R(P) can be used as an estimate of the rectilinearity of P. The mapping R(P) has the following desirable properties: - any polygon P has the estimated rectilinearity R(P) which is a number from (0, 1]; - R(P)=1 if and only if P is a rectilinear polygon, i.e., all interior angles of P belong to the set {?/2, 3?/2}; - inf P?? R(P) = 0, where ? denotes the set of all polygons; - a polygon's rectilinearity measure is invariant under similarity transformations. A simple procedure for computing R(P) for a given polygon P is described as well.

/pdf/a-rectilinearity-measurement-for-polygons-57wuqm5qvy.pdf

A Rectilinearity Measurement for Polygons

Extremal problems on convex lattice polygons in sense of l p -metrics

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Jovisa D. Zunic

Papers

Rectilinearity measurements for polygons

A Convexity Measurement for Polygons

A Rectilinearity Measurement for Polygons

Extremal problems on convex lattice polygons in sense of l p -metrics

A new measure for the rectilinearity of polygons