Fisheye projections from spherical mapsWritten by Paul Bourke
"sphere2fish" takes a full spherical map and generates fisheye views given a center position for the fisheye, optionally an up vector, and an aperture from 0 to 360 degrees. In addition, the user may choose the level of antialiasing (supersampling) and an option to create a circularly bounds fisheye (traditional) or a rectangularly bound fisheye (the later is usually only appropriate for smaller aperture angles). The application is in the form of a UNIX style commandline interface, a TGA file is expected for the input image (24 or 32 bit RGB), the output fisheye image is written to standard output. The usage message is given below.
Usage: sphere2fish [options] sphereimage Options -w n width and height of the fisheye image, default = 500 -t n fisheye aperture (degrees), default = 180 maximum is 360 degrees -c x y center longitude and latitude of fisheye, default = 0 0 degees -u x y z up vector, default = (0,0,1) required for latitude = +- 90 degrees (poles) -f rectangular fisheye instead of circular -a n antialiasing level, default = 1 (no antialising)
The conventioned used with the program as drawn below. In particular, zero longitude and latitude are taken to be in the center of the spherical image.
The following spherical image will be used to illustrate (and test) various capabilities of the fisheye generator.
The following is a spherical projection stitched from 50 images using AutoPano Pro. Only a 1/2 hemisphere is captured. The original spherical projection image is 22000x11000 pixels.
In this case only one fisheye can be captured. If the full spherical projection was captured (only requiring twice the number of individual images) then a fisheye pointing in any direction can be sampled. The original fisheye images can be up to 10,000 pixels square.
Converting Images from Panoramic to DomeWritten by Paul Bourke
Example images courtesy (and copyright) Astro Copy Service, Planetarium Augsburg, Germany
See also Angular fisheye projections.
The following will discuss the conversion of panoramic images into those suitable for display onto a dome, in particular, angular fisheye as used by the majority of planetarium domes. There are a number of panoramic image formats, they all use the same horizontal axis which ranges from 0 to 2 pi. There are however a number of vertical distortions, the two most common are considered here. One is often called a radial panoramic where the vertical axis is considered to lie on the surface of a sphere, the other is a linear panoramic where the vertical axis results from a standard perspective projection. This second is the most common, the image is obtained by projecting onto a cylinder about the camera.
As with most mappings the goal is to estimate the colour for each pixel in the destination image. The distination image in this case is the angular fisheye, the colour estimate will be determined by the corresponding pixels in the source (panoramic) image. In general there isn't a single pixel in the input image corresponding to a particular pixel in the destination image. For best results it is usual to find the closest pixel in the input image for a range of positions within each pixel in the destination image, these are averaged together to determine the final estimate of the colour. This is commonly called antialiasing, the simplest form of which is to estimate the colour by averaging over a 2x2 or 3x3 grid within each pixel.
The basic idea is to find the mapping between a coordinate system in the angular fisheye and a coordinate system in the panoramic image. The convenient coordinate system in the angular fisheye is "r" (the distance from the center of the pixel to the pixel in question) and the angle "phi" (angle of the vector to the pixel). The convenient coordinate system in the panoramic image is the same angle "phi" (the vertical axis of the panoramic), in both images this angle varies from 0 to 2 pi. The vertical axis of the panoramic is proportional to the "r" in the angular fisheye. This is illustrated in the following figure.
The conversion of the two types of panoramic image will be illustrated by transforming the following test pattern. This will be done for three values of thetamax, that is, the panoramic images will be assumed to vary vertically from 0 to 30, 60, and 90 degrees.
The hole in the center for all but the 90 degree case reflects the lack of image data from thetamax to 90 degrees which is the centeral portion of the fisheye image.Linear panoramic
The most obvious feature of this case is the extreme distortion that occurs as the fisheye tends to 90 degrees. Of course, while the distortion seems extreme below that is because the test image has a equal spacing grid, something that would not normally occur in a 90 degree panoramic. A normal 90 degree panoramic would appear very distorted itself and the process of turning that into a dome image would correct for the distortion.
The following is a linear 45 degree angular fisheye of the panoramic shown at the top of this page.
pan2sph panfilename [options] Options: -t n set max theta on vertical axis of panoramic, 0...90 (default: 45) -a n set antialias level, 1 upwards, 2 or 3 typical (default: 2) -w n width of the dome image, height = width (default: 512) -s use sine function correction (default: off) -r n rotation angle, 0...nx (default: 0) -f flip insideout (default: off) -bg r g b set background colour, 0...255 each (default: 0 0 0)
Usage: pano2fish [options] fisheyeimage Options -w n fisheye image width and height, default = -1 -r r1 r2 inner and outer radius of the fisheye image -h h1 h2 top and bottom panoramic edges -a n antialiasing level, default = 1 (no antialising) -d change direction of panoramic -p n rotate by n degrees -c clear region outside fisheye radius