Reconstructions from zero crossings in scale space

In computer vision, the one-parameter family of images obtained from the Laplacian-of-a-Gaussian-filtered version of the image, parameterized by the width of the Gaussian, has proved to be a useful data structure for the extraction of feature data. In particular, the zero crossings of this so-called scale-space data are associated with edges and have been proposed by D. Marr (1982) and others as the basis of a representation of the image data. The question arises as to whether the representation is complete and stable. The authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations. They formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error, and they present results showing that the reconstruction is possible but can be unstable. They further show that the method applies when gradient data along the zero crossings are included in the representation, and they demonstrate empirically that the reconstruction is then stable. >

[1]  Alan L. Yuille,et al.  Fingerprints Theorems , 1984, AAAI.

[2]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[3]  F. John.  Partial differential equations , 1967 .

[4]  B. Logan.  Information in the zero crossings of bandpass signals , 1977, The Bell System Technical Journal.

[5]  Shlomo Shamai,et al.  Reconstruction of nonperiodic two-dimensional signals from zero crossings , 1987, IEEE Trans. Acoust. Speech Signal Process..

[6]  T. Poggio,et al.  Fingerprints theorems for zero crossings , 1985 .

[7]  A. Rosenfeld,et al.  Edge and Curve Detection for Visual Scene Analysis , 1971, IEEE Transactions on Computers.

[8]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[9]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[10]  S W Zucker,et al.  Receptive fields and the representation of visual information. , 1986, Human neurobiology.

[11]  Benjamin Kedem.  Zero-Crossings Analysis. , 1986 .

[12]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Andrew P. Witkin,et al.  Uniqueness of the Gaussian Kernel for Scale-Space Filtering , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[15]  Yehoshua Y. Zeevi,et al.  Image reconstruction from zero crossings , 1986, IEEE Trans. Acoust. Speech Signal Process..

[16]  Benjamin B. Kimia,et al.  Deblurring Gaussian blur , 2015, Comput. Vis. Graph. Image Process..

[17]  C. Enroth-Cugell,et al.  The contrast sensitivity of retinal ganglion cells of the cat , 1966, The Journal of physiology.

[18]  L. S. G. Kovasznay,et al.  Image Processing , 1955, Proceedings of the IRE.

[19]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[20]  Thomas S. Huang,et al.  Image Representation by Sign Information , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  John Daugman,et al.  Six formal properties of two-dimensional anisotropie visual filters: Structural principles and frequency/orientation selectivity , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  T. Poggio,et al.  A computational theory of human stereo vision , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[23]  Jae S. Lim,et al.  Signal reconstruction from Fourier transform sign information , 1985, IEEE Trans. Acoust. Speech Signal Process..

[24]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Alan V. Oppenheim,et al.  Reconstruction of Multidimensional Signals from Zero Crossings* , 1986, Topical Meeting On Signal Recovery and Synthesis II.