Geometric Distortions - Sunwaysite

Geometric Distortion

Notes on rectilinear lens distortions and fisheye* (update)

2 June 2017

In September 2014 Samyang released stereographic projection UWA for 135 format that is part of fisheye lens family. The stereographic diagonal fisheye maintains principle of fisheye projection where the linear geometry is bent but unlike the classic fisheyes, it leaves objects shapes in original form. The regular projection fisheye lenses deform shape of objects at the periphery beyond recognition. This is especially apparent in the corners where the fisheye effect naturally draws attention of a viewer (due to the compression). This doesn’t have to be a negative effect but it distinctly separates rendition of a stereographic UWA from typical equisolid angle and equidistant fisheye lenses.

As there are no elements of extreme rendition with stereographic projection, it creates its own category among the UWA lenses.

Another projection useful and intuitive for object recognition (in the entire image) is perspective projection of corrected UWA. The shapes of objects are deformed but easily recognisable and intuitively correct (though exaggerated) while the linear geometry in the image does not change.

It is debatable which projection produces more natural representation of the scene. The stereographic projection preserves shapes of objects locally in remarkably truthful representation and virtually unchanged but it curves the whole space. It exaggerates “its sense” in often intuitively correct way that is in line with our natural perception.

This makes both of these projection types closely related and fit for realistic representation and distinct from non-stereographic projection fisheye.

The fact, however remarkable, has obviously no a priori bearings on artistic, photographic or aesthetic choice and preferences as apparent from the subjective nature of most applications.

26 November 2014

Most rectilinear lenses add some kind of geometric distortion to the picture as they project capture of a subject. One of the most prominent distortions is changed perspective and it is particularly noticeable with the wide and ultra wide angles. It is a kind of distortion that influences remarkably well transition from our own perception of the scene based on our brain and two lenses cooperation to a one lens capture. Prominent changes in perspective and its exaggeration are also extending the tools for a richer expression.

Another kind of geometric distortion of a lens is barrel distortion. Unlike the regular and predictable changes in perspective, this kind of radial distortions are often seen as an optical flaw of a lens and that because it is much less necessary for the design and thus more changeable from lens to lens.

Because the barrel distortion is also a perspective distortion of a sort we can see these two interacting. We will notice that the barrel distortion works its own way towards offsetting the perspective distortion effects by compressing the near corner geometry while making the central area visually more apparent by enlarging it. A mild degree of the barrel distortion in particular can be then often viewed as a beneficial and desirable effect for the overall projection of the scene. It is fine that it is retaining its reputation of a flaw as it is a matter of degree, and it is also less useful universally as a tool. I myself tune my corrections for barrel distortion for each image separately and with some care. Correction that I apply is often partial  and many times I am leaving it without any correction whereas sometimes I will choose to correct it fully.

Geometric distortion working in opposite direction of the barrel is pincushion distortion. This curves of the space in the image I correct often fully and in some instances almost always, for example, when typical wildlife is the subject. For other subjects, this I again tend to weight individually.

Moustache types of distortions that are less symmetrical work towards the elongated corner geometry and similar (compression) less effectively but even they can be found beneficial for rendering characteristics of a lens by a photographer. Their irregular curves though often command a default correction.

Observing meaningful details when processing a photograph can make a difference. And just as, e.g. careful framing where the each millimeter plays its role, the symmetrical distortions can help in creating a photograph that conveys its content precisely the way we want. Realising this can also change our view of excessive distortions that inhere in the design of affected lenses because the partial corrections using suitable software have only minimal negative impact on the rendering and resolution quality. And it can, on the other hand, add to the means for a thoughtful processing of digital images using mild distortions optimally for the intent of the final execution.

© HSunway

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