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SIGGRAPH 2009 Computational photography

Invertible Motion Blur in Video

Amit Agrawal, Yi Xu, and Ramesh Raskar

The idea

Change the exposure. Recover the detail.

Motion blur in a single photograph can lose information that deconvolution cannot recover. By changing the exposure time across successive video frames, we create jointly invertible blur: detail missing in one frame is supplied by another. The approach estimates motion and segments moving objects against textured backgrounds using ordinary cameras.

Three motion-blurred photographs of a moving car, the deblurred result, and motion streaks
Varying the exposure across captured frames allows sharp detail to be recovered from a moving car.
01

Making blur
invertible

Comparison of conventional exposure, coded exposure, and varying-exposure video for invertible motion blur
PSF null-filling: frequencies lost in one frame are recovered from other frames with different exposure times.

A conventional exposure produces box-shaped motion blur with zeros in its frequency response. These missing frequencies make deblurring ill-posed. Coded exposure can make a single image’s blur invertible by fluttering the shutter, but requires a specialized exposure pattern and manual point-spread function (PSF) estimation in the original approach.

Our method uses PSF null-filling: successive frames have different exposure times and therefore different blur functions. Frequencies lost in one frame are filled by other frames, making the combined response null-free. Multiple images also make PSF estimation and foreground segmentation easier, without hardware modifications.

02 / Results

Deblurring through partial occlusion

Recovering a sharp moving object against a textured background, even when an object in the foreground partially blocks it.

A moving toy car partially occluded by a flower, with a sharp reconstruction and a synthesized composite
A flower occludes the moving toy car in all four captured photographs. The user marks the occluder in the first image; occluded pixels are excluded during deblurring. The composite keeps the moving object sharp while blurring the occluder.

03 / Additional examples

Faces and rotational motion

The approach works with standard DSLR exposure bracketing. PSF null-filling also extends to non-linear motions that become linear after image rectification.

Blurred photographs of a person standing up and the recovered sharp face
Faces: three photographs captured with Auto Exposure Bracketing on a Canon Digital Rebel XT, using exposures of 1/10, 1/13, and 1/8 seconds. Deblurring recovers facial features clearly.
Rotating CD images rectified into polar coordinates, deblurred, and transformed back to a sharp CD image
Rotating CD: polar-coordinate rectification converts rotational motion into linear blur. Deblurring followed by inverse rectification recovers a sharp image.
04

Abstract

We show that motion blur in successive video frames is invertible even if the point-spread function (PSF) due to motion smear in a single photo is non-invertible. Blurred photos exhibit nulls (zeros) in the frequency transform of the PSF, leading to an ill-posed deconvolution. Hardware solutions to avoid this require specialized devices such as the coded exposure camera or accelerating sensor motion.

We employ ordinary video cameras and introduce the notion of null-filling along with joint-invertibility of multiple blur-functions. The key idea is to record the same object with varying PSFs, so that the nulls in the frequency component of one frame can be filled by other frames. The combined frequency transform becomes null-free, making deblurring well-posed. We achieve jointly-invertible blur simply by changing the exposure time of successive frames.

We address the problem of automatic deblurring of objects moving with constant velocity by solving the four critical components: preservation of all spatial frequencies, segmentation of moving parts, motion estimation of moving parts, and non-degradation of the static parts of the scene. We demonstrate several challenging cases of object motion blur including textured backgrounds and partial occluders.

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