Quantitative Measures of Change Based on Feature Organization: Eigenvalues and Eigenvectors

Sarkar, Sudeep; Boyer, Kim L.

doi:10.1006/cviu.1997.0637

Cited by 144 publications

(135 citation statements)

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“…Here we use a result due to Sarkar and Boyer [20] who have shown how matrix factorisation methods can be used to locate the set of edges which partition the nodes into distinct perceptual clusters. One way of viewing this is as the search for the permutation matrix which re-orders the elements of A into non-overlapping blocks.…”

Section: Selecting the Number Of Modesmentioning

confidence: 99%

“…Unfortunately, when the elements of the matrix A are not binary in nature, then this is not a straightforward task. However, Sarkar and Boyer [20] have shown how the positive eigenvectors of the matrix of linkweights can be used to assign nodes to perceptual clusters. Using the Rayleigh -Ritz theorem, they observe that the scalar quantity x t A ð0Þ x; where A (0) is the initial weighted adjacency matrix, is maximised when x is the leading eigenvector of A.…”

Section: Selecting the Number Of Modesmentioning

confidence: 99%

“…At this point it is worth pausing to review the way in which Sarkar and Boyer [20] use the eigenvectors of the adjacency matrix to assign nodes to clusters. In an attempt to render the clustering method robust to noise, they allow up to 5% of the components of the eigenvectors to flip sign.…”

Section: Selecting the Number Of Modesmentioning

confidence: 99%

“…Each plot contains three curves. In both cases, the dotted (leftmost) curve is the result of applying the Sarkar and Boyer [20] method to the raw link-weight matrix. This method assigns lines to clusters based on the same-sign eigenvectors as described in Section 3.3.…”

Section: Synthetic Imagesmentioning

confidence: 99%

“…One of the most popular methods here is to use ideas from spectral graph theory to locate the salient relational structure. For instance, both Sarkar and Boyer [20] and Perona and Freeman [17] have used the eigenstructure of a perceptual affinity matrix to find disjoint subgraphs that represent the main arrangements of segmental entities. Finally, it is worth mentioning that several authors have used similar algorithms based on eigenvalues of an affinity matrix to iteratively segment image data.…”

Section: Introductionmentioning

confidence: 99%

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An expectation–maximisation framework for segmentation and grouping

Robles-Kelly

Hancock

2002

Image and Vision Computing

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This paper casts the problem of perceptual grouping into an evidence combining setting using the apparatus of the EM algorithm. We are concerned with recovering a perceptual arrangement graph for line-segments using evidence provided by a raw perceptual grouping field. The perceptual grouping process is posed as one of pairwise relational clustering. The task is to assign line-segments (or other image tokens) to clusters in which there is strong relational affinity between token pairs. The parameters of our model are the cluster memberships and the pairwise affinities or link-weights for the nodes of a perceptual relation graph. Commencing from a simple probability distribution for these parameters, we show how they may be estimated using the apparatus of the EM algorithm. The new method is demonstrated on line-segment grouping problems where it is shown to outperform a non-iterative eigenclustering method. q

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Section: Selecting the Number Of Modesmentioning

confidence: 99%

Section: Selecting the Number Of Modesmentioning

confidence: 99%

Section: Selecting the Number Of Modesmentioning

confidence: 99%

Section: Synthetic Imagesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An expectation–maximisation framework for segmentation and grouping

Robles-Kelly

Hancock

2002

Image and Vision Computing

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Enhancing signals from buried Roman structures in Magnetometer data by combining continuous wavelet transform and tensor voting

Jungmann

Dolenz

Clauser

et al. 2017

Archaeological Prospection

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In this paper, a processing chain is proposed for enhancing larger‐scale building structures in magnetometer data using the continuous wavelet transform for extracting the horizontal location, depth, and homogeneity (or shape) of subsurface objects. Even though the values estimated from our data do not clearly describe the archaeological site, they are used as a filter step for removing objects whose depth and homogeneity fall outside a predefined range. This yields a binary map, where valid points represent the horizontal source positions of magnetic anomalies. In a second step, curvilinear subsets of points are identified on a larger scale by the tensor voting framework indicating archaeological relevant structures, such as arcs and lines. Here, a point casts votes on neighbouring points and their values depend on the distance, and relative position of the points. All votes are summed up and the final value discriminates, whether a certain point (and therefore a magnetic source) is part of a salient curve (e.g. arc, line). Thresholding removes points with lower values while keeping those with larger values. Although the result shows many geometric features, it still needs to be combined with other data, e.g. from aerial photography or excavations. In combination, the extracted features continue those structures in the aerial photograph, thus expanding the knowledge about the archaeological site.

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