{"type":"ScholarlyArticle","title":"Dynamically Quantized Pyramids","authors":[{"name":"Kenneth R. Sloan Jr.","slug":"kenneth-r-sloan-jr","given":"Kenneth R. Sloan","family":"Jr.","affiliation":"Department of Computer Science University of Rochester Rochester , NY 14627"}],"abstract":"Dynamically Quantized (DQ) spaces have been developed [O'Rourke] in response to the need for high-precision, high-dimensional Hough·like transforms. [Ballard; Sloan and Ballard] Their purpose is to cover a parameter space with a limited number of accumulators in such a way that fine precision is maintained where it is needed. O'Rourke's solution to this problem is to maintain a binary tree of cells. Each cell covers an n-dimensional rectangular region of the space. Under certain conditions, the cell may be split along a particular dimension, and two sons created. Under complementary conditions, sets of cells may merge. Cell splitting is relatively simple, but the process of cell merging is quite complicated, for reasons which are explored extensively in [O'Rourke]. The solution presented here is based on a pyramid data structure, in which the number and connectivity (between fathers and sons) of cells is fixed . This data structure has the advantage that its resource allocation is fixed, and the cells and their connections may be reduced to a hardware implementation (e.g., in VLSI.) The customary difficulty with the pyramid is that the boundaries of the cells (and hence the spatial resolution) are fixed, also. In this Dynamically Quantized Pyramid (DQP), the boundaries of the cells are continually modified by means of a hierarchical warping process. Essentially, each cell tries to track the mean position of data points in its part of the space. This estimate of the local mean is used to define the boundaries of the cell's sons. An experimental implementation has been built and subjected to various distributions (spatial and temporal) of data. The resulting quantizations are shown and discussed.","doi":null,"url":"https://ijcai.org/proceedings/1981/140","pdf":"https://ijcai.org/proceedings/1981/0140.pdf","markdown":"https://ijcai.org/proceedings/1981/140.md","bibtex":"https://ijcai.org/proceedings/1981/bibtex/140","volume":{"slug":"1981","title":"Proceedings of the Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1981","url":"https://ijcai.org/proceedings/1981/","year":1981,"location":"Vancouver, British Columbia, Canada","dates":"24-28 August 1981","editors":"Roger C. Schank","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Vision: Low-level","track":"Vision: Low-level","number":140,"pages":{"first":734,"last":735},"keywords":[],"videos":[],"references":[{"position":1,"raw":"Ballard, D.H Generalizing the Hough Transform to detect arbitrary shapes, Pattern Recognition, Vol. 13, No.2, pp. 111-122, 1981.","title":"H Generalizing the Hough Transform to detect arbitrary shapes","authors":"D Ballard","year":"1981","venue":"Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"O'Rourke, Joseph Dynamically Quantized Spaces Applied to Motion Analysis, Proceedings: /JCA/-81, Vancouver, Canada, August 1981.","title":"Joseph Dynamically Quantized Spaces Applied to Motion Analysis","authors":"O'rourke","year":"1981","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"Sloan, K.R., Jr. and D.H. Ballard Experience with the Generalized Hough Transform, Proceedings: 5th International Conference on Pattern Recognition, pp. 174-179, December 1980.","title":"Experience with the Generalized Hough Transform","authors":"K R Sloan, D H Jr, Ballard","year":"1980","venue":"Proceedings: 5th International Conference on Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"Tanimoto, S.L. and T. Pavlidis A hierarchical data structure for picture processing, Computer Graphics and Image Processing, vol 4, no. 2, pp. 104-119, 1975.","title":"A hierarchical data structure for picture processing","authors":"S L Tanimoto, T Pavlidis","year":"1975","venue":"Computer Graphics and Image Processing","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}