Parsing scale-space and spatial stability analysis

Abstract The scale-space S(x, σ) of a signal I(x) is defined as the space of the zero-crossings from {∇2G(σ)* I(x)}, where G is a Gaussian filter. We present a new method for parsing scale-space, spatial stability analysis, that allows the localization of region boundaries from scale space. Spatial stability analysis is based on the observation that zero-crossings of region boundaries remain spatially stable over changes in filter scale. It is shown that spatial stability analysis leads to an edge detection scheme with good noise resilience characteristics and that it can lead to improvements in “shape from texture” methods.

[1]  Tomaso A. Poggio,et al.  On Edge Detection , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Katsushi Ikeuchi,et al.  Shape from Regular Patterns , 1984, Artif. Intell..

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

[4]  Ramesh C. Jain,et al.  Invariant surface characteristics for 3D object recognition in range images , 1985, Comput. Vis. Graph. Image Process..

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

[6]  Michael J. Brooks,et al.  The variational approach to shape from shading , 1986, Comput. Vis. Graph. Image Process..

[7]  David Marr,et al.  VISION A Computational Investigation into the Human Representation and Processing of Visual Information , 2009 .

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

[9]  Stanley M. Dunn,et al.  Efficient Recovery of Shape from Texture , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  John Ronald Kender,et al.  Shape from texture , 1981 .

[11]  Terry Caelli,et al.  Coding images in the frequency domain: Filter design and energy processing characteristics of the human visual system , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

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

[13]  Eric L. W. Grimson,et al.  From Images to Surfaces: A Computational Study of the Human Early Visual System , 1981 .

[14]  Itzhak Katz.  Coaxial stereo and scale-based matching , 1985 .

[15]  Azriel Rosenfeld,et al.  Digital Picture Processing, Volume 1 , 1982 .

[16]  R. Haralick,et al.  The Topographic Primal Sketch , 1983 .

[17]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

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

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

[20]  R. Haralick,et al.  The Topographic Primal Sketch and Its Application to Passive Navigation , 1983 .

[21]  G Moraglia,et al.  On the detection of signals embedded in natural scenes , 1986, Perception & psychophysics.

[22]  Wolfram H. H. J. Lunscher,et al.  Optimal Edge Detector Design II: Coefficient Quantization , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Zhi-Qiang Liu,et al.  Filter-based models for pattern classification , 1988, Pattern Recognit..

[24]  Terry Caelli,et al.  Discrimination thresholds in the two-dimensional spatial frequency domain , 1983, Vision Research.

[25]  D Marr,et al.  A computational theory of human stereo vision. , 1979, Proceedings of the Royal Society of London. Series B, Biological sciences.

[26]  J. Canny.  Finding Edges and Lines in Images , 1983 .

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