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Invariant Moments for Shape Recognition in Image Processing

This term project explores the concept of invariant moments in image processing, focusing on their stability for shifting, scaling, and rotating digital shapes. The project delves into the calculations and comparisons of invariant moments to minimize errors for accurate shape recognition. Implemented solution involves rotating images at 5-degree intervals, sampling, and comparing invariant moments to identify shapes effectively. Simulate the process to test recognition accuracy.

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Invariant Moments for Shape Recognition in Image Processing

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  1. Shape Recognition by Invariant Moments Image Processing Fundamentals Term Project 2004-2005 Autumn

  2. Prepared by • Asım Güneş 040020606 • Fuat Kılıç 040000103 • Çağrı Ergül 040000115 • Ercan Zer 040000074

  3. What is Invariant Moments ? • For a 2-D continuous function f(x,y), the moment of order (p+q) is defined as

  4. Rotating • For rotating we use the central moments:

  5. In central moments

  6. Normalized Central Moments • These moments are stable for shifting and scaling.

  7. Seven Invariant Moments of HU - 1 • In 1962 Hu was described seven moments for shifting, scaling and rotating.

  8. Seven Invariant Moments of HU -2

  9. Problem • Normally these invariant moments do not change. • But we are studying in digital medium so there are some quantization errors. • When we rotate or change the size of the image these errors occur. • These errors are maximum in (45+k∏/2) degrees and minimum in (k∏/2) degrees.

  10. Finding Rotating Error Error =

  11. Graph of Rotating Error

  12. Our aim is MINIMIZING THE ERRORS • Solution is Rotating the image for 5 degrees intervals between the 0-45 degrees and sampling the image. We save invariant moments of these samples. Then we compare these values of invariant moments with the invariant moments of other images, we get the samples which has minimum difference. By this way we recognize the image.

  13. Reading Configuration File Bird;shape/bird.bmp; Dolphin;shape/dolphin.bmp; Flag;shape/flag.bmp; Anchor;shape/anchor.bmp; .... Importing sample images Sampling images in every 5 degrees shapes.conf Calculating invariant moments of every sample Invariant Moment Database Saving calculations to database dbInitialize

  14. Reading image Calculating Invariant Moment of image Invariant Moment Database Comparing Invariant Moment from DB Result compareImage(filename)

  15. IT’S TIME TO SIMULATE

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