Logical/Linear Operators for Image Curves

We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and Boolean logic. A family of these operators appropriate for measuring the low-order differential structure of image curves is developed. These L/L operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld. Tangential conditions guarantee continuity, while normal conditions select and categorize contrast profiles. The resulting operators allow for coarse measurement of curvilinear differential structure (orientation and curvature) while successfully segregating edge-and line-like features. By thus reducing the incidence of false-positive responses, these operators are a substantial improvement over (thresholded) linear operators which attempt to resolve the same class of features. >

[1]  Steven W. Zucker,et al.  Toward discrete geometric models for early vision , 1994 .

[2]  J. Movshon,et al.  Length summation in simple cells of cat striate cortex , 1984, Vision Research.

[3]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[4]  J. P. Jones,et al.  An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. , 1987, Journal of neurophysiology.

[5]  Edward H. Adelson,et al.  The Design and Use of Steerable Filters , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Berthold K. P. Horn.  Understanding Image Intensities , 1977, Artif. Intell..

[7]  R. Young.  GAUSSIAN DERIVATIVE THEORY OF SPATIAL VISION: ANALYSIS OF CORTICAL CELL RECEPTIVE FIELD LINE-WEIGHTING PROFILES. , 1985 .

[8]  G. Birkhoff,et al.  A survey of modern algebra , 1942 .

[9]  H. Kalmus.  Biological Cybernetics , 1972, Nature.

[10]  R. Goodstein.  Boolean algebra , 1963 .

[11]  Manfred H. Hueckel.  An Operator Which Locates Edges in Digitized Pictures , 1971, J. ACM.

[12]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[13]  Thomas O. Binford,et al.  On Boundary Detection , 1970 .

[14]  R. J. Watt,et al.  Mechanisms responsible for the assessment of visual location: Theory and evidence , 1983, Vision Research.

[15]  Steven W. Zucker,et al.  The computational connection in vision: Early orientation selection , 1986 .

[16]  R. Haralick.  Digital Step Edges from Zero Crossing of Second Directional Derivatives , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Jitendra Malik,et al.  Detecting and localizing edges composed of steps, peaks and roofs , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[18]  Azriel Rosenfeld,et al.  On Models for Line Detection , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  D. Burr,et al.  Feature detection in human vision: a phase-dependent energy model , 1988, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[20]  H. Weinberger,et al.  Maximum principles in differential equations , 1967 .

[21]  Steven W. Zucker,et al.  The Organization Of Curve Detection: Coarse Tangent Fields And Fine Spline Coverings , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[22]  P. Perona,et al.  Detecting and localizing edges composed of steps , 1990 .

[23]  Steven W. Zucker,et al.  The Local Structure of Image Discontinuities in One Dimension , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Pietro Perona.  Steerable-scalable kernels for edge detection and junction analysis , 1992, Image Vis. Comput..

[25]  Steven W. Zucker,et al.  Two Stages of Curve Detection Suggest Two Styles of Visual Computation , 1989, Neural Computation.

[26]  J. Movshon,et al.  Spatial summation in the receptive fields of simple cells in the cat's striate cortex. , 1978, The Journal of physiology.

[27]  Peter E. Hart,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[28]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Steven W. Zucker,et al.  The Organization Of Curve Detection: Coarse Tangent Fields And Fine Spline Coverings , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

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

[31]  P. Lennie,et al.  Spatial frequency analysis in the visual system. , 1985, Annual review of neuroscience.

[32]  J. Koenderink,et al.  The Shape of Smooth Objects and the Way Contours End , 1982, Perception.