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Lecture-07 - Fall2012 Tuesday,September11,2012 ECE6258...

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9/11/2012 1 Multidimensional Digital Signal Processing Prof. Ghassan AlRegib School of Electrical and Computer Engineering Georgia Institute of Technology ECE 6258 Digital Image Processing Fall 2012 Tuesday, September 11, 2012 ECE 6258 Fall 2012 Lessons from Last Time Sampling Interval Matrix: 2 Ghassan AlRegib © Georgia Tech 11 21 12 22 x x x x  ECE 6258 Fall 2012 Outline Generalized Sampling Downsampling & Upsampling Decimation & Interpolation Quantization of images Ghassan AlRegib © Georgia Tech 3 ECE 6258 Fall 2012 Lessons from Last Time Sampling Interval Matrix: 4 Ghassan AlRegib © Georgia Tech 11 21 12 22  
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9/11/2012 2 ECE 6258 Fall 2012 Lessons from Last Time Sampling density 5 Ghassan AlRegib © Georgia Tech t t u u I     1 |det | |  1 () ( ( ) ) | a F F uF u F ݇ ݇ ECE 6258 Fall 2012 Question Q: What shapes or regions of support can be sampled with the below lattice and have the same sampling efficiency of 100%? 6 Ghassan AlRegib © Georgia Tech ECE 6258 Fall 2012 Sampling Sampling, in general, is understood to mean the representation of a discrete version of a continuous signal. But if we select subsamples from an already sampled image, then we are performing sampling as well. 7 Ghassan AlRegib © Georgia Tech ECE 6258 Fall 2012 Downsampling 8 Ghassan AlRegib © Georgia Tech 1 D: Downsampling by a factor means: contains every M th sample of Sampling density of sampling density of M [] [ ] g nf M n g n f n 1 gn M f n
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9/11/2012 3 ECE 6258 Fall 2012 Downsampling 9 Ghassan AlRegib © Georgia Tech 2 D: In rectangular downsampling: i.e. Keeping every M th sample of every N th row
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Lecture-07 - Fall2012 Tuesday,September11,2012 ECE6258...

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