Motion blur — where it appears
Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.
The disc and the streak
A frame integrates over the pupil and over the exposure at once. Hold the point's depth and the patch is exactly the streak of its centres with one disc slid along it, to 1.8 × 10⁻⁵ of its own width. Let it recede over the same exposure and the disc's radius falls by 3.7 along the streak, and the patch departs from any single kernel by 16 pixels.
One depth per sample is not enough
A depth buffer keeps a single distance at each sample, so a post-process blur can only ask how far away the thing at this pixel is. Across an occluding edge that answer is two depths and an occlusion, and the gather it produces differs from the pupil's own integral by 70 per cent of full scale over a band eleven pixels wide.
Turning and travelling blur different worlds
A subject 8 m away crosses the frame at 4 m/s, and the camera keeps it sharp over a thirtieth of a second. Turn to follow it and every still thing blurs by the same 13.5 px, whatever its depth. Travel beside it and the still world blurs as one over its depth — 49 px at 2 m, 1.5 px at 64 m — while everything moving with the subject is sharp at every depth.
A camera on a bend is sharp on a circle
A camera car rounding a 50 m bend at 10 m/s, aimed into the bend, blurs the still world everywhere except at the bend's centre — and under a pixel from 42 m to 63 m along its axis. Off the axis the sharp place comes nearer as the cosine of the bearing, on the circle through the camera and the centre. Above the ground only the vertical line through the centre stays sharp. Aimed along the road, the camera has no sharp distance at all.
A rolling frame on a bend is right at its centre
Read a camera car's frame row by row as it rounds a bend and every still point moves — except the bend's centre, at every height, and the horizon row, at every depth. Each mark's displacement is its streak scaled by its row time, so the rolling frame is undistorted wherever the global one is sharp. And the usual repair makes it worse: a gyroscope that undoes the turn row by row puts 0.73 px back into the centre and is a net loss everywhere nearer than twice the bend's radius.
A rolling frame on a bend is a coarse curvature gauge
Read row by row on a bend, a frame leans every vertical by an amount proportional to one over its range less one over the bend's radius, so posts at several ranges lie on a straight line that crosses zero at the radius — exactly, to a thousandth of a metre. Off the axis the zero moves to R·cos of the bearing, the circle on which a camera on a bend is sharp. As a gauge it is coarse: one frame's eight posts read a 50 m bend as 45 m (35–74) with tops placed to half a pixel, and sixteen frames as 51 m (47–55). The slower the sensor reads, the better it measures the road.
A tracked post reads the bend, if the speed is known
A rolling camera aimed at a bend's centre passes across its roadside posts rather than towards them: in half a second a post twelve metres out moves from 12.0 to 12.8 metres away and its lean changes by five per cent. Followed through those sixteen frames it is one lean read sixteen times, and one lean is a ratio of the car's speed to the bend's radius. With the speed known it reads the radius as 49.9 metres (48.1–52.9), closer than eight posts in a single frame; with it unknown, it reads nothing. Aimed forty-five degrees ahead, the camera closes on the post, its lean doubles, and one post gives both.
Named alongside it
The objects these essays reach for when they reach for this one.
Moving viewpointExposureParallaxSensorcamera trackAperturecentre of projectionCircle of confusionConvolutionDepth cueEntrance pupilinstrument limit