Presentation on theme: "Optimizing and Learning for Super-resolution"— Presentation transcript:
1Optimizing and Learning for Super-resolution Lyndsey C. Pickup, Stephen J. Roberts& Andrew ZissermanRobotics Research Group, University of Oxford
2The Super-resolution Problem Given a number of low-resolution imagesdiffering in:geometric transformationslighting (photometric) transformationscamera blur (point-spread function)image quantization and noise.Estimate a high-resolution image:
14Generative Model High-resolution image, x. y1 y2 y3 y4 Low-resolution imagesW4W3W2W1Registrations, lighting and blur.
15Generative Model We don’t have: We have: Geometric registrations Point-spread functionPhotometric registrationsSet of low-resolution input images, y.
16Maximum a Posteriori (MAP) Solution y1y2y3y4W4W3W2W1xStandard method:Compute registrations from low-res images.Solve for SR image, x, using gradient descent.[Irani & Peleg ‘90, Capel ’01, Baker & Kanade ’02, Borman ‘04]
17What’s new We solve for registrations and SR image jointly. We also find appropriate values forparameters in the prior term at thesame time.Hardie et al. ’97: adjust registration while optimizing super-resolution estimate.Exhaustive search limits them to translation only.Simple smoothness prior softens image edges.i.e. given the low-res images, y, we solve for the SR image x and the mappings, W simultaneously.y1y2y3y4W4W3W2W1x
18Overview of rest of talk Simultaneous ApproachModel detailsInitialisation techniqueOptimization loopLearning values for the prior’s parametersResults on real images
19Maximum a Posteriori (MAP) Solution y1y2y3y4W4W3W2W1xImage x.Corrupt with additive Gaussian noise.Warp, with parameters Φ.Blur by point-spread function.Decimate by zoom factor.y
20Details of Huber PriorHuber function is quadratic in the middle, and linear in the tails.ρ (z,α)p (z|α,v)Red: large αBlue: small αProbability distribution is like a heavy-tailed Gaussian.This is applied to image gradients in the SR image estimate.
21Details of Huber PriorAdvantages: simple, edge-preserving, leads to convex form for MAP equations.Solutions as α and v vary:Ground Truthα=0.1 v=0.4α=0.05 v=0.05α=0.01 v=0.01α=0.01 v=0.005Edges are sharperToo much smoothingToo little smoothing
22Advantages of Simultaneous Approach Learn from lessons of Bundle Adjustment: improve results by optimizing the scene estimate and the registration together.Registration can be guided by the super-resolution model, not by errors measured between warped, noisy low-resolution images.Use a non-Gaussian prior which helps to preserve edges in the super-resolution image.Remember, the classical approach is…. Fix ‘n’ solve.
23Overview of Simultaneous Approach Start from a feature-based RANSAC-like registration between low-res frames.Select blur kernel, then use average image method to initialise registrations and SR image.Iterative loop:Update Prior ValuesUpdate SR estimateUpdate registration estimate
24ML-sharpened estimate InitialisationAverage imageUse average image as an estimate of the super-resolution image (see paper).Minimize the error between the average image and the low-resolution image set.Use an early-stopped iterative ML estimate of the SR image to sharpen up this initial estimate.ML-sharpened estimate
25Optimization Loop Update prior’s parameter values (next section) Update estimate of SR imageUpdate estimate of registration and lighting values, which parameterize WRepeat till converged.
27Learning Prior Parameters α, ν Split the low-res images into two sets:Use first set to obtain an SR image.Find error on validation set.
28Learning Prior Parameters α, ν Split the low-res images into two sets:Use first set to obtain an SR image.Find error on validation set.But what if one of the validation images is mis-registered?
29Learning Prior Parameters α, ν Instead, we select pixels from across all images, choosing differently at each iteration.We evaluate an SR estimate using the unmarked pixels, then use the forward model to compare the estimate to the red pixels.
30Learning Prior Parameters α, ν Instead, we select pixels from across all images, choosing differently at each iteration.We evaluate an SR estimate using the unmarked pixels, then use the forward model to compare the estimate to the red pixels.
31Learning Prior Parameters α, ν To update the prior parameters:Re-select a cross-validation pixel set.Run the super-resolution image MAP solver for a small number of iterations, starting from the current SR estimate.Predict the low-resolution pixels of the validation set, and measure error.Use gradient descent to minimise the error with respect to the prior parameters.
32Results: Eye ChartMAP version: fixing registrations then super-resolvingJoint MAP version with adaptation of prior’s parameter values
34Results: Groundhog Day The blur estimate can still be altered to change the SR result. More ringing and artefacts appear in the regular MAP version.Blur radius = 1Blur radius = 1.4Blur radius = 1.8Regular MAPSimultaneous
40ConclusionsJoint MAP solution: better results by optimizing SR image and registration parameters simultaneously.Learning prior values: preserve image edges without having to estimate image statistics in advance.DVDs: Automatically zoom in on regions with a registrations up to a projective transform and with an affine lighting model.Further work: marginalize over the registration – see NIPS 2006.