Moiré artifacts and other forms of aliasing often appear in electronic imaging systems due to insufficient sampling of the optical images. Spatial aliasing occurs when the optical image bandwidth exceeds that of the image detector. Spatial aliasing manifests itself when a TV host wears a fine-striped shirt, producing distracting moirés.

George's moirés

George's moirés

Temporal aliasing occurs when the temporal bandwidth of the imaged scene exceeds the frame rate of the camera. Temporal aliasing manifests itself in the wagon wheel illusion in a Western movie. A rotating wagon wheel will appear to freeze or even to reverse its rotation.

Why don’t biological systems experience aliasing — or do they? Does the eye or brain circuits exhibit aliasing and moiré phenomena?

The human eye appears to avoid spatial aliasing by supersampling the optical signal: the point spread function of the eye optics covers several photoreceptors. What limits the resolution of the eye is the optics. The cornea, aqueous humor, the lens, vitrous humor, and three layers of retinal cells in front of the photoreceptors blur the signal and efficiently remove the very high-frequency content in the image. In addition, the arrangement of photoreceptors is not strictly regular as happens in a CCD chip for example. Thus chances of producing a spatial moiré pattern in the eye are nil.

However, temporal or spatiotemporal aliasing may occur, probably in motion processing areas of the visual cortex. One manifestation of this glitch is the motion reversal illusion sometimes perceived when a spoked wheel accelerates and decelerates through a range of RPMs. Skeptical that this could be the result of the stroboscopic effect of electric lighting, I made a black-and-white pinwheel and spun it. Even in daylight, at some rotation rates, I perceived subtle and transient episodes of illusory reversal. You can try this for yourself.

I spun this wheel to reproduce the rotation reversal illusion.

Spinning wheel to reproduce the rotation reversal illusion.

Is this evidence that the visual system has a semi-regular ‘frame rate’ similar to video and film cameras? I found it hard to believe. Temporally subsampled signals indicate inefficiencies undercutting the quantum efficiency (ie overall sensitivity) of the system, a problem that’s too easily fixed by introducing additional blurring (low-pass filtering) to limit the bandwidth before sampling. Temporal blurring is something very easy for cells to do and evolution would have long found a way to blur the signal, even if vision did work in regular discontinuous frames. There has to be something else to account for the illusory motion reversal.

In a recent paper by Kline and Eagleman (2008) in the Journal of Vision titled “Evidence against the snapshot hypothesis of illusory motion reversal”, the authors staged a series of experiments that argued against the snapshot hypothesis (frame-rate hypothesis).
The experiments support the rivalry hypothesis of the illusory motion reversal, ie that “the continuous stimulation of one direction of motion eventually causes rivalry with the opposite direction of motion, and the balance of the rivalry eventually tips, engendering the perception of reversed motion”. In other words, motion detection is hypothesized to consist of multiple motion detectors that each have undersampled spatiotemporal responses, many of which produce aliasing. Normally, those motion detectors that detect correct motion are stimulated stronger than their aliased counterparts resulting in correct perception. However, in continuous exposure, the strongly stimulated detectors desensitize and the aliased detectors get their opinions heard. That’s the putative mechanism, but no specific circuits responsible for this illusion have yet been described.


George’s moirés


The Chicago Tribune’s Seinfeld 10 years later story gave Jason Alexander a serious case of the moirés.

Remember Nyquist: smoothen before subsampling.

But could this have been intentional? The miorés make the jacket much more expressive. Was this a deliberate artistic trick? Have moirés been used by digital photographers to enhance the three-dimensional feel of the image?

Before exploring moiré patterns more systematically and mathematically, let’s look at a few examples.

Most moirés are incidental: they arise naturally when two or more gratings, sheets of fabric, wire screens, fences, or dot screens are superposed.

Fence moiré, by Prof. David Eppstein at UC Irwine

In signal processing and imaging, moiré patterns are often known as aliasing. They arise when the sampling rate of a digitized signal is too low to accurately represent the signal. This effect may be a big nuisance in photography and television. In this case in the role of the two gratings play the periodic features in the image and the regular arrangement of pixels in the camera.

Moiré patterns are responsible for adding funky colors to Al Gore’s collar in this photo, arguably improving its appearance:

These aliasing artifacts can be easily resolved by either increasing the sampling resolution or by applying proper filtering techniques prior to sampling as described by the Nyquist theorem.

Moiré patterns are commonly treated as a problem. However, they also have many useful applications. For example, their ability to magnify small offsets is exploited for strain and deformation analysis of materials by means of moiré interferometry.

The intentional synthesis of moirés appears to be largely unexplored. The most interesting and sophisticated examples of moiré art I have found to date are animated pictures in children’s books:

Animated Illusion, Solved!Funny videos are here

Invariably, the words magic and amazing are used to describe moiré phenomena, even the most basic ones.

These examples are but a small fraction of what could be done with moirés. Through this blog, I would like to expand the definition of moirés and their applications.