TY - JOUR

T1 - A unified scheme for detecting fundamental curves in binary edge images

AU - Asano, Tetsuo

AU - Katoh, Naoki

AU - Tokuyama, Takeshi

N1 - Funding Information:
This work was partially supported by the Grant-in-Aid of Ministry of Education, Science and Culture of Japan.

PY - 2001/3

Y1 - 2001/3

N2 - We present a unified scheme for detecting digital components of various planar curves in a binary edge image. A digital component of a curve is the set of input edge points from each of which the horizontal or vertical distance to the curve is at most 0.5. Our algorithm outputs all curve components containing at least k points (k is a given threshold) in O(nd) time (if d≥2) and linear space, where n is the number of points, and d is a measure that reflects the complexity of a family of curves; for example, d=2,3 and 5 for lines, circles and ellipses, respectively. For most of the popular families of curves, our only primitive operations are algebraic operations of bounded degree and comparisons. We also propose an approximate algorithm for computing an approximation solution with error ratio ε=1-α (called an α-sensitive solution), whose time complexity is O((t/ε)d-1n), which is very efficient if the threshold-ratio t=n/k is small.

AB - We present a unified scheme for detecting digital components of various planar curves in a binary edge image. A digital component of a curve is the set of input edge points from each of which the horizontal or vertical distance to the curve is at most 0.5. Our algorithm outputs all curve components containing at least k points (k is a given threshold) in O(nd) time (if d≥2) and linear space, where n is the number of points, and d is a measure that reflects the complexity of a family of curves; for example, d=2,3 and 5 for lines, circles and ellipses, respectively. For most of the popular families of curves, our only primitive operations are algebraic operations of bounded degree and comparisons. We also propose an approximate algorithm for computing an approximation solution with error ratio ε=1-α (called an α-sensitive solution), whose time complexity is O((t/ε)d-1n), which is very efficient if the threshold-ratio t=n/k is small.

KW - Algorithm

KW - Arrangement

KW - Digital curve

KW - Image recognition

UR - http://www.scopus.com/inward/record.url?scp=0035276766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035276766&partnerID=8YFLogxK

U2 - 10.1016/S0925-7721(01)00002-5

DO - 10.1016/S0925-7721(01)00002-5

M3 - Article

AN - SCOPUS:0035276766

VL - 18

SP - 73

EP - 93

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 2

ER -