Technology - What is it?
Fisheye-Hemi is a plug-in filter which provides correction for hemispheric fisheye lens distortion.
Fisheye Hemispheric lenses provide a broader view of the world than is possible with any other lens. Until now, the primary correction option available to the photographer was to render these images using rectilinear mapping techniques. These methods have many drawbacks, such as distortion of people and loss of resolution and data.
The Fisheye-Hemi filter provides an aesthetically pleasing and natural view of the image using a unique mapping technology. Fisheye-Hemi provides a more normal view of people when photographed at acceptable distances. It improves the resolution of the image by including more of the original pixels (in comparison to a rectilinear view), displays the intended composition and framing, and straightens vertical lines.
How does Fisheye-Hemi work?
Let's begin with a basic understanding of what a fisheye lens does and how the eye perceives the information.
Light projects conically into the human eye. The cornea and lens are similar to a fisheye lens. The light is projected onto the curved retina. The human brain uses complex mathematics to correctly interpret the objects that you see into a three dimensional image.
To a person holding a camera, the surrounding space appears to be a sphere centered on the camera. The process of taking a picture projects this sphere inward onto a flat (planar) surface. This surface could be film or a digital sensor representing a planar surface. Fisheye-Hemi provides an improved way of mapping the surface of the sphere to the planar surface.
Figure 1 - Light entering the eye
Figure 2 - Cartographer Map of the Earth
The mapping process has an exact analogy to cartography. Although the surface of the earth is two dimensional, those two dimensions bend into a three dimensional sphere. Ideally this is represented onto the surface of a globe. The cartographer must map the sphere to a flat paper. There is no “right” way to map a sphere to a plane.
In photography, there is still the sphere around the camera, the real world, and still the flat surface of a print or computer screen that must accommodate that sphere with perceived accuracy. In map making, a small part of the globe can be easily flattened on a flat surface. Most lenses cover moderate angles. These images can be easily projected onto a flat surface. Modern advances in optics have given photographers better ultra wide angle lenses, such as the modern fisheye lens. There is a need to better handle the distortions these lenses produce.
Most lenses are “rectilinear”, which means “straight line”. A pinhole camera renders a “perfect” rectilinear projection. With such a projection, a line at any arbitrary orientation maps to a straight line on the print. The radial distance an object appears from the center of the print and is proportional to the tangent of the angle from the normal of the front lens element. With small angles from the normal, this tangential function is nearly proportional to the angle and non-distorting in all aspects. However at larger angles the tangential function grows rapidly, hitting a singular infinity point at plus/minus 90 degrees = 180 degree total angle. For this reason a rectilinear projection can not handle total angles approaching 180 degrees.
Even with more moderate angles of 90 degrees corner to corner, the tangential expansion distorts the aspect of an object at the edge of a picture. For example, with a 20mm lens on a 35mm film camera, a person standing at the extreme left edge of the image would appear almost twice as wide relative to height as if they were standing in the middle of the frame. Because weight is proportional to size, direct measurement of their image would suggest that they had grown from 150 pounds in the center of the image, to 600 pounds if they were at the edge of the image. Often mathematicians define lens distortion exclusively in terms of how straight lines are bent, however photographers know that there are other aspects of distortion.
Some lenses are built to other projections. By far the most common non-rectilinear lens is the equal-solid-angle “fisheye”. This projection is defined such that the solid angle occupied by an object in front of the lens maps to an image with the same area no matter where the object is in the field of view. If used in meteorology, for example, the area of a cloud on the print is proportional to the “size” of the real cloud projected to a sphere centered on the camera, and therefore invariant with respect to the camera aim. This projection does not follow a tangential expansion, and is very comfortable at 180 degrees. Legacy commercial fisheyes have reached 220 degrees, mathematically impossible angles with a rectilinear.
Rather than expanding with a tangential function, the fisheye projection actually compresses progressively with larger angles. For example, if an observer were at the center of a transparent globe showing the earth’s geography, using a hypothetical very wide equal-solid-angle fisheye lens aimed at the north pole, then Australia would appear to expand east-west in the corner of the frame as the lines of longitude were straightened on the flat film, like smashing an orange peal to a flat surface, as they are in a polar map projection. However the fisheye projection would have a concurrent compression in the north-south axis so the area of Australia remained the same on the film. Thus Australia would appear very elongated and flattened, even though the area is correct. In the same way a fisheye lens distorts people standing at the edges by compressing them horizontally and making them unnaturally tall.
A fisheye projection also bends any straight line that does not pass through the optical center. Thus a person appears very tall and thin on the edge of a fisheye image and is bent into a half-moon shape.
For many years, fisheye lenses have been relegated mostly to special effects because of visual distortions. With the advent of wide-spread digital image processing, computer remapping of fisheye lens images is now practical for many photographers, and a number of products are available to “un-distort” fisheye images. However these existing products un-distort a fisheye in a technical sense by mapping to a rectilinear projection. The standard definition of “distortion” is how much lines are bent, and rectilinear is technically a “distortion less” projection.
No matter how mathematically perfect at making lines straight, forcing a rectilinear projection at the extreme angles encompassed by a fisheye creates problems. A major problem is the distortion of people. Further, the extreme expansion of a rectilinear projection magnifies the edge of the image to reveal lens resolution problems. Rectilinear compresses the center of the image which looses detail the lens has been able to capture. Therefore, making images look un-sharp and grainy. The rectilinear projection is unable to map large areas at the edges of the photographed fisheye image within the rectangular bounds of the originally captured image. The result crops out edge detail and makes it very difficult for a photographer to frame and compose in the viewfinder.
The fisheye lens (depending on the camera sensor size) can typically capture a full 180 degree field measured from corner to corner of the sensor. It is an ultra-wide angle lens. It captures a hemisphere or half of a sphere as seen by the lens:
Figure 3 - Typical Hemispheric Lens
A rectilinear lens in photography renders images with straight features (all lines straight) versus being curved. A good rectilinear lens will exhibit no barrel or pincushion distortion.
Figure 4 - Hemisphere of view as seen by the lens
The fisheye lens was originally developed for astronomy to capture much of the sky. They were called 'whole sky lenses' in the early days.
Definition of Rectilinear Correction – Fisheye lenses can be mapped in software back to a rectilinear space. Rectilinear means that all lines are straight with no curves. Many rectilinear projections will deliver only the center of the full image that was seen by the lens. About one third of the captured information is discarded in this projection. The window demonstrates what most rectilinear projections deliver to the end user. The other information is discarded.
Definition of Cylindrical Correction– Please review the drawing below and recognize the mathematics of a cylindrical projection from a sphere:
X= constant*alpha (angle)
Imagine a cylinder wrapped around a globe (fisheye hemisphere in this case) and how the data could be mapped to the cylinder and then rolled flat.
Most projections are ‘distortion free’ only in the center of the projected image. Objects near the top and bottom are distorted. Please refer to Figure 6 representing a typical rectilinear projection. Fisheye-Hemi produces a more aesthetically pleasing image to the average person.
Figure 5 - Cylindrical Projection
Figure 6 - Typical Rectilinear Projection
A typical fisheye lens delivers images in what is called ‘barrel distortion’ which means that the image appears to be mapped around all or part of a spherical object.
Pincushion distortion is the opposite of barrel distortion. The magnification of the image increases with increasing distance from the optical axis. This effect typically occurs with low end or poor telephoto lenses.
What is different about Fisheye-Hemi projections?
Fisheye-Hemi is designed to provide a mapping function to spatially project an image made with a fisheye lens into an image that minimizes distortion of humans and other objects.
Another design point is to minimize distortion of people and other objects while preserving straight vertical lines and, preserving image detail, It also aids composition in the viewfinder by preserving detail up to the top and bottom edges of the original fisheye image.
What does all of this mean to me?
The human eye likes images to be aesthetically pleasing. You prefer the faces to be normal, the bodies straight, the lines straight, minimal loss of image detail, and high resolution.
Fisheye-Hemi delivers aesthetically pleasing images.
Fisheye-Hemi: It's for people...