## Improving Resolution by Image Registration – CVGIP 1991 – Part 1

- Image Resolution depends → Physical Characteristics of Sensor
- Optics
- Density of detector elements
- Spatial Response of detector elements
- Resolution ↑
- Sensor modification → X (not available sometimes)
- Sampling Rate ↑ → More samples from a sequence of displaced pictures
- Estimate of the sensor ‘s spatial response
- Solution of the paper → Iterative algorithm to increase image resolution + Image Registration with sub-pixel accuracy
- Low resolution gray level and color images
- De-blurring a single blurred
- Literature Review
- Tsai & Huang [10] → Frequency domain→Only translations considered
- Gross[6]→ Assumption: Imaging process is known, relative shifts to the input pictures are known → Merging low-res pictures over a finger grid using interpolation → Single blurred picture of higher spatial sampling →Convolution with restoration filter obtained by pseudo-inverse of matrix of blur operator → De-blurred picture →Only translations considered
- Peleg et al.[16,12]→Estimate an initial guess of the higher res image →Simulate the imaging process (Assumption: known)→Set of simulated low res images →Error function between the actual and simulated low res images→Minimize Error iteratively → Stall/Max Iters
- +: Noise-free images
- -: Highly sensitive to noise, Slow to converge
- Analogy with Computer Aided Tomography (CAT)
- CAT → Images are reconstructed from their projections in many directions→Back-projection method
- SR→Each low-res pixel is a “projection” of a region in the scene →The size is determined by the imaging blur→Similar to Back-projection method*
- Imaging process: Quantization of the blurred image f with additive noise n
- g_k → k-th observation image frame
- f → original scene
- h → blurring operator
- n_k → additive noise
- s_k → nonlinear quantization function + displacement of k-th frame
- (x,y)→ center of receptive field( in f) of the detector whose output is g(k)(m,n)

- Receptive Field (in f) of a detector

- Output: g_k(m,n)
- Center: (x,y)
- Shape → Region of support of the blurring operator h
- Displacement = translations + rotations
- (x_0k,y_0k) → Translation of k-th frame
- theta_k → rotation of k-th frame
- s_x, s_y → sampling rate in the x and y direction

- Enhancing the resolution of color images → YIQ representation
- Monochrome SR algorithm may then be applied separately to each component
- Gray-level images are processed together with Y component image sequence
- Obtaining the parameters of Imaging process: Image Registration → Iterative Refinement → Recovering the Blur
- Image Registration
- Karen et al[12] based on [13] for this model → Horizontal shift a + Vertical shift b + rotation theta between images g1 and g2 → Valid for small displacements
- Trick: g2 is translated and rotated of g1 → Expanding Sin and Cos by their Taylor’s series (first two terms) → Expanding g1 to it’s own Taylor series (first term) → Error function between g1 and g2 (overlapping parts)→ Minimize Error → Motion parameters (a,b,theta)

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