Abstract

This paper presents an algorithm for constructing the convex envelope of an object, based on an analysis of the derivative of the chain code of its boundary. The construction process consists of selecting boundary points with a positive derivative that satisfy a proposed convexity condition. Such points determine the vertices of a closed polygon that is the convex envelope of the object. A method is proposed for estimating the number of holes and the convexity coefficient, based on the ratio of the perimeters of the object and of its convex envelope.

© 2010 Optical Society of America

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  1. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N. J., 2002; Tekhnosfera, Moscow, 2005).
  2. V. Kovalevsky, “Discrete topology and contour definition,” Pattern Recogn. Lett. 2, 281 (1984).
    [CrossRef]
  3. C. E. Kim, “Digital convexity, straightness lines and convex polygons,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 618 (1982).
    [CrossRef]
  4. J. Sclansky, “Measuring concavity on rectangular mosaic,” IEEE Trans. Comput. 21, 1355 (1972).
    [CrossRef]
  5. A. Rosenfeld, “Digital straight line segment,” IEEE Trans. Comput. 23, 1264 (1974).
    [CrossRef]
  6. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978; Mir, Moscow, 1982), vol. 2.
  7. R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973; Mir, Moscow, 1976).
  8. H. Freeman, “On the encoding of arbitrary geometric configurations,” IEEE Trans. EC 10, No. 5, 260 (1961).
  9. H. Freeman, “Computer processing of line drawing images,” ACM Comput. Surv. 6, No. 1, 57 (1974).
    [CrossRef]

1984 (1)

V. Kovalevsky, “Discrete topology and contour definition,” Pattern Recogn. Lett. 2, 281 (1984).
[CrossRef]

1982 (1)

C. E. Kim, “Digital convexity, straightness lines and convex polygons,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 618 (1982).
[CrossRef]

1974 (2)

A. Rosenfeld, “Digital straight line segment,” IEEE Trans. Comput. 23, 1264 (1974).
[CrossRef]

H. Freeman, “Computer processing of line drawing images,” ACM Comput. Surv. 6, No. 1, 57 (1974).
[CrossRef]

1972 (1)

J. Sclansky, “Measuring concavity on rectangular mosaic,” IEEE Trans. Comput. 21, 1355 (1972).
[CrossRef]

1961 (1)

H. Freeman, “On the encoding of arbitrary geometric configurations,” IEEE Trans. EC 10, No. 5, 260 (1961).

Duda, R. O.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973; Mir, Moscow, 1976).

Freeman, H.

H. Freeman, “Computer processing of line drawing images,” ACM Comput. Surv. 6, No. 1, 57 (1974).
[CrossRef]

H. Freeman, “On the encoding of arbitrary geometric configurations,” IEEE Trans. EC 10, No. 5, 260 (1961).

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N. J., 2002; Tekhnosfera, Moscow, 2005).

Hart, P. E.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973; Mir, Moscow, 1976).

Kim, C. E.

C. E. Kim, “Digital convexity, straightness lines and convex polygons,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 618 (1982).
[CrossRef]

Kovalevsky, V.

V. Kovalevsky, “Discrete topology and contour definition,” Pattern Recogn. Lett. 2, 281 (1984).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978; Mir, Moscow, 1982), vol. 2.

Rosenfeld, A.

A. Rosenfeld, “Digital straight line segment,” IEEE Trans. Comput. 23, 1264 (1974).
[CrossRef]

Sclansky, J.

J. Sclansky, “Measuring concavity on rectangular mosaic,” IEEE Trans. Comput. 21, 1355 (1972).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N. J., 2002; Tekhnosfera, Moscow, 2005).

ACM Comput. Surv. (1)

H. Freeman, “Computer processing of line drawing images,” ACM Comput. Surv. 6, No. 1, 57 (1974).
[CrossRef]

IEEE Trans. Comput. (2)

J. Sclansky, “Measuring concavity on rectangular mosaic,” IEEE Trans. Comput. 21, 1355 (1972).
[CrossRef]

A. Rosenfeld, “Digital straight line segment,” IEEE Trans. Comput. 23, 1264 (1974).
[CrossRef]

IEEE Trans. EC (1)

H. Freeman, “On the encoding of arbitrary geometric configurations,” IEEE Trans. EC 10, No. 5, 260 (1961).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

C. E. Kim, “Digital convexity, straightness lines and convex polygons,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 618 (1982).
[CrossRef]

Pattern Recogn. Lett. (1)

V. Kovalevsky, “Discrete topology and contour definition,” Pattern Recogn. Lett. 2, 281 (1984).
[CrossRef]

Other (3)

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N. J., 2002; Tekhnosfera, Moscow, 2005).

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978; Mir, Moscow, 1982), vol. 2.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973; Mir, Moscow, 1976).

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