Digital Image Processing Lecture 11 Image Restoration Prof

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Digital Image Processing Lecture 11: Image Restoration Prof. Charlene Tsai

Digital Image Processing Lecture 11: Image Restoration Prof. Charlene Tsai

Review n In last lecture, we discussed techniques that restore images in spatial domain.

Review n In last lecture, we discussed techniques that restore images in spatial domain. q q n Mean filtering Order-statistics filering Adaptive filering Gaussian smoothing We’ll discuss techniques that work in the frequency domain. 2

Periodic Noise Reduction n n We have discussed low-pass and high-pass frequency domain filters

Periodic Noise Reduction n n We have discussed low-pass and high-pass frequency domain filters for image enhancement. We’ll discuss 2 more filters for periodic noise reduction q q Bandreject Notch filter 3

Bandreject Filters n Removing a band of frequencies about the origin of the Fourier

Bandreject Filters n Removing a band of frequencies about the origin of the Fourier transform. q Ideal filter where D(u, v) is the distance from the center, W is the width of the band, and D 0 is the radial center. 4

Bandreject Filters (con’d) q Butterworth filter of order n q Gaussian filter 5

Bandreject Filters (con’d) q Butterworth filter of order n q Gaussian filter 5

Bandreject Filters: Demo Original corrupted by sinusoidal noise Butterworth filter Fourier transform Result of

Bandreject Filters: Demo Original corrupted by sinusoidal noise Butterworth filter Fourier transform Result of filtering 6

Notch Filters n n n Reject in predefined neighborhoods about the center frequency. Due

Notch Filters n n n Reject in predefined neighborhoods about the center frequency. Due to the symmetry of the Fourier transform, notch filters must appear in symmetric pairs about the origin. Given 2 centers (u 0, v 0) and (-u 0, -v 0), we define D 1(u, v) and D 2(u, v) as 7

Notch Filters: plots ideal Butterworth Gaussian 8

Notch Filters: plots ideal Butterworth Gaussian 8

Reducing the effect of scan lines 9

Reducing the effect of scan lines 9

Notch Filters (con’d) q Ideal filter q Butterworth filter q Gaussian filter 10

Notch Filters (con’d) q Ideal filter q Butterworth filter q Gaussian filter 10

How to deal with motion or out-of-focus blurring ? Original Blurred by motion 11

How to deal with motion or out-of-focus blurring ? Original Blurred by motion 11

Convolution Theory: Review Filter (degradation function) Degraded image n n n Original image Knowing

Convolution Theory: Review Filter (degradation function) Degraded image n n n Original image Knowing the degradation function H(u, v), we can, in theory, obtain the original image F(u, v). In practice, H(u, v) is often unknown. We’ll discuss briefly one method of obtaining the degradation functions. For interested readers, please consult Gonzalez, section 5. 6 for other methods. 12

Estimation of H(u, v) by Experimentation for out-of-focus n If equipment similar to the

Estimation of H(u, v) by Experimentation for out-of-focus n If equipment similar to the one used to acquire the degraded image is available, it is possible, in principle, to obtain the accurate estimate of H(u, v). q q q Step 1: reproduce the degraded image by varying the system settings. Step 2: obtain the impulse response of the degradation by imaging an impulse (small dot of light) using the same system settings. Step 3: recalling that FT of an impulse is a constant (A) Degraded impulse image What we want Strength of the impulse 13

Estimation of H(u, v) by Exp (con’d) An impulse of light (magnified). The FT

Estimation of H(u, v) by Exp (con’d) An impulse of light (magnified). The FT is a constant A G(u, v), the imaged (degraded) impulse 14

Undoing the Degradation Filter (degradation function) Degraded image n n Original image (what we’re

Undoing the Degradation Filter (degradation function) Degraded image n n Original image (what we’re after) Knowing G & H, how to obtain F? Two methods: q q Inverse filtering Wiener filtering 15

Inverse Filtering n In the simplest form: n See any problems? q Noise –

Inverse Filtering n In the simplest form: n See any problems? q Noise – random function Division by small values can produce very large values that dominate the output. Original Inverse filtering using Butterworth filter 16

Inverse Filtering (con’d) n n Solutions? There are two similar approaches: q q Low-pass

Inverse Filtering (con’d) n n Solutions? There are two similar approaches: q q Low-pass filtering with filter L(u, v): Thresholding (using only filter frequencies near the origin) D(u, v) being the distance from the center 17

Inverse Filtering: Demo Full filter d=40 d=70 d=85 18

Inverse Filtering: Demo Full filter d=40 d=70 d=85 18

Inverse Filtering: Weaknesses n Inverse filtering is not robust enough. q Doesn’t explicitly handle

Inverse Filtering: Weaknesses n Inverse filtering is not robust enough. q Doesn’t explicitly handle the noise. n It is easily corrupted by the random noise. n The noise can completely dominate the output. 19

Wiener Filtering n n What measure can we use to say whether our restoration

Wiener Filtering n n What measure can we use to say whether our restoration has done a good job? Given the original image f and the restored version r, we would like r to be as close to f as possible. One possible measure is the sum-squareddifferences Wiener filtering: minimum mean square error: Specified constant 20

Comparison of Inverse and Wiener Filtering n n n Column 1: blurred image with

Comparison of Inverse and Wiener Filtering n n n Column 1: blurred image with additive Gaussian noise of variances 650, 65 and 0. 0065. Column 2: Inverse filtering Column 3: Wiener filtering 21

Summary n Removal of periodic noise: q q n Bandreject Notch filter Deblurring the

Summary n Removal of periodic noise: q q n Bandreject Notch filter Deblurring the image: q q Inverse filtering Wiener filtering 22

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