Exploring Perspective

Here are a few thoughts about one of the most useful tools we have, to give the impression of depth in a photograph. It is reproduced from my Blog, and I hope it clarifies the use and meaning of perspective effects in a photograph.

Previous cultures understood pictorial perspective, but in its mathematical form, linear perspective is generally believed to have been devised about 1415 by the architect Filippo Brunelleschi (1377–1446) and codified in writing by the architect and writer Leon Battista Alberti (1404–1472), in 1435 (De pictura [On Painting]).

But, Brunelleschi, Alberti, and others only understood one point perspective, the simplest pictorial form of perspective. We have just one point where the sightlines converge. Central perspective, however, is so violent and intricate a deformation of the normal shape of things that it came about only as the result of prolonged exploration and in response to very particular cultural needs. Curiously, the distortions imposed by perspective on the real, tactile world are so successful that modern viewers only note them when pointed out.

If we construct a perspective drawing, or use perspective in a photograph, the angle of view is a question of proportion, that can be explained by tracing an image on a window whilst looking through a small hole at a fixed distance. A simple illustration explains the concept nicely. It is obvious that the angle of view and the steepness of the sightlines are infinitely variable.

Quoting a pamphlet on the use of perspective in Renaissance painting, published by the British National Gallery, we can understand that sometimes we need to depart from pure geometric, or mathematical models:

“Optical illusion does not necessarily depend on mathematical absolutes and, with a few important exceptions such as Piero della Francesca, it seems that painters were more concerned with achieving a level of visual plausibility than with the rigorous application of theoretical models. Perspective was designed to fulfil the needs of the picture (not vice versa), and a series of other conditions and criteria were at stake: the knowledge, skill and aesthetic preferences of the artist, the demands of patrons, the ways in which the site might determine the viewpoint, and the requirements of the subject matter. Thus, a painting which has often been considered a perspectival manifesto, Masaccio’s ‘Trinity’ fresco, has been shown to bend the rules of one-point mathematical perspective, probably because it looked better that way”

Construction of a One-Point perspective drawing

Sight lines for Leonardo da Vinci's The Last Supper

Simple 1 point perspective

Two-point perspective, necessary to show objects set at an oblique angle to the viewer, took another century to evolve. The first known diagram of the two-point perspective by Jean Pélérin, in his De Artificiali perspectiva (1505), which was also the first printed treatise on perspective. With two-point perspective, there are two vanishing points on the horizon line. This creates the illusion of depth and space

Simple 2 point perspective

Two-point perspective is probably a much more useful, than one point perspective, if we want to create an illusion of a three-dimensional object in a photograph. But it is harder to control and unwanted perspective effects can creep in to make a picture look unnatural.

Three-point perspective is a type of perspective that uses three vanishing points. It is used to draw objects that are above or below the viewer’s eye level, such as skyscrapers or bridges. In three-point perspective, the lines that are parallel to each other in the real world converge to three different points on the horizon line. Three-point perspective is closely connected to two-point perspective, and is generally unwelcome in Architectural photography. Three-point perspective often appears as “key stoning” in a photograph.

Simple 3 point perspective

Let's look at some real world examples. With Aldo Rossi's Ossario in Modena as an example. I made three pictures with one, two and three point perspective.

1 point perspective

2 point perspective

3 point perspective

When we look at a reasonably low building like the one above, our brain applies key stone correction, and we see the vertical walls as being vertical.

A shift lens can help us produce pictures with one or two point perspective. It allows us to shift our eyesight convergence point in any direction.

Upward shift moves the single convergence point upwards

But we can also shift the convergence point both upwards and sideways, to keep the horizontal and vertical line s parallel, and create un unusual perspective effect

Exaggerated 2 point perspective for dramatic effect.

2 point perspective

One of the problems that happened when try and classify how many points they have in an image it that there are an infinite number of points to create an image in a 2D print.
If we look at the first to create the lighted areas in front of the building they have their own VP. It only really comes to play when dealing with simple objects.
The placement of an objects within the frame will create the theoretical VP. Take a car parked parallel to the street it will follow the VP of the street, skew that car to 10 degrees from the street and now we need VP to create its relationship of that car in a 2d print.

I introduced the most simple cases, to show how the basic principles of perspective drawing and photography using perspective effects . We can see in the drawing below that we can have many vanishing points in a scene. But most of the time one or two point perspective for the main subject are sufficient.

The principle piece of furniture obeys two point perspective. Think of all the secondary objects as separate entities using two or three point perspective in this case.

Using shift in a lens is the equivalent of asymmetric cropping on a bigger sensor.

If don't want to pay for a 100+MP medium format camera, and despise any perspective corrections during post processing, there's an easy alternative to using a shift lens:

Use the same camera positioning, but a shorter focal lenght so to get your subject into frame.
Later, just crop the excess surroundings from your photo.

Yep, that will cost ya a couple of pixels in resolution.
But is that really a problem in the age of 200MP smartphones?

This thread is not about shift lenses. It is about perspective, in the visual arts.

Shift lenses are a tool I use to get one and two point perspective in a photograph. It allows me to frame the scene I want, without having to guess future cropping.

here is a quote from James Ewing from his textbook Follow the Sun. A book aimed at professionals and students and considered a standard text for Architectural photography.

"You might ask yourself "Do I really need an expensive tilt shift lens" Can't I just correct the perspective later in Photoshop?" The answer is yes you could correct it later, but the tilt shift lens allows you to see and feel the perspective of the images you are shooting. The final crop and ultimately the entire composition will be totally different in a shot that is corrected in post. If you cannot see the image while you are shooting you cannot control the composition and therefore you cannot effectively interpret the building. Correcting the perspective during post production causes a significant loss of sharpness and detail. The Tilt shift lens gives you accurate, sharp controlled images."

I think this says it all.

I started my photography with shift lenses, with a €300 D700 and a €300 Nikon 28mm PC lens. If you have a mirrorless camera you can easily adapt the €300 Nikon PC or Canon 24 ( early version) and have a very effective low cost ability to use shift lenses. My complete set of shift lenses cost me much less than many people pay for just one long lens for wildlife or sport.

Shift lenses seem to incite a lot of "lens hate" for some reason on photo forums. I cannot see the problem with using the right lens for the photo.

But as usual the thread has quickly gone off topic. This is a tread about perspective and any lens on any camera, as long as it is perfectly level can exploit one and two point perspective.

One could use the same argument for primes vs zooms -- rather than use a zoom, just use a wider prime and crop. Depending on how much you're cropping, just like depending on how much you're correcting for perspective, you can take quite a hit in IQ.

Of course, PC lenses can be a bit of a pain. So far as I'm aware, they're all primes and all manual focus. That's pretty inconvenient for a lot of people. Then again, primes can be a bit of a pain for a lot of people. Suffice it to say, there are pros and cons to all these options, just like everything else. We simply need to be aware that our preference is usually not universal, and people choosing differently aren't necessarily doing it because they're unaware that there's a better way -- we all balance absolute IQ and convenience differently.

Well, you mentioned shift lenses in the OP.

You seem to think that cropping an image changes the perspective in it?

Cropping an image does change the framing, not the perspective.

Also, shifting a lens does change the framing, while the camera position (and direction) determines the perspective of the photo, shift lens or not.

Nice illustration of the process of creating a perspective drawing.

Making the comparison with taking a photograph, the peephole represents the camera lens and the distance between the peephole and the window glass represents the focal length (of a very large format camera).

I would think that most people would say that the perspective is different in a photo with obvious keystoning and the same photo taken with a shift lens to eliminate keystoning (or with the keystoning eliminated by software).

Sure, but that's entirely a question of where the camera was pointed at, parallel to ground level (no keystoning) or upwards|downwards.

And yes, perspective corrections can also be done in software.

PS: no shift lens required in either case.

I agree. However, we have to be very careful to define what we mean by the direction in which the camera was pointing. Most people will assume that the camera is pointing towards the centre of the picture (which is true in most cases). In this case, however, we mean the direction of the optical axis (because the image has been cropped).

Careful definitions are needed to avoid misunderstanding and confusion.

Always infer, never assume.
That's a problem with images that don't have center of perspective in the center of the picture.

Especially horizontal shifts in a photo seem somewhat weird to our perception, while we can more easily adapt for keystone corrected photos (as our brain is used to an horizon near eye level).

I mentioned shift lenses because they are the best way of controlling perspective in a photograph. A large format camera with full movements is even better.

You put words in my mouth. Cropping, shifting does not change the perspective in a picture, that is pretty obvious. Shifting changes the convergence point, cropping changes the angle of view.

Yes it is a good illustration of a pretty simple concept.

Here is a link to a couple of old but still very valid books about artistic perspective( Valid until 29/7)

I cannot see anything weird about this picture with a horizontal and vertical off axis convergence point.

BTW. diagonal shift is very difficult to replicate with software correction, where the horizontal and vertical lines are parallele.

Yup, most viewers will at first assume optical centres would match, thus its perceived kinda odd if that assumption is erroneous.