Autostereoscopic lenticular image

Introduction

Stereoscopic systems present the viewer with an image of a 3D object such that it appears to have "real" depth. The wide variety of techniques all involve presenting different views of the 3D object independently to each eye hence simulating stereopis. Traditional stereoscopic systems employ an apparatus that keeps the left and right eye images directed solely at the appropriate eye, examples are helmets or shutter glasses.

How lenticular images work

Parallax barrier methods were known about in the early 1900's, they include the parallax stereogram and the related parallax panoramagram. These will be discussed first as they are easier to initially understand. The parallax stereogram consists of a fine vertical grating placed in front of a specially designed image. The grating is normally made of an opaque material with fine transparent vertical splits at a regular spacing. Each transparent slit acts as a window to a vertical slice of the image placed behind it, the exact slice depends on the position of the eye.

Parallax panoramagrams use not just a pair of images but a larger number of number images. These can be arbitrary images or images in a time ordered sequence in which case tilting the panoramagram will give the impression of motion. In this discussion we will consider the case where the images are from a number of appropriately ordered viewpoints about a focal point, the result will be a depth perception. The image behind the barrier is formed by laying strips from each subimage next to each other.

The viewer can move their head from side to side and see different aspects of the 3D scene, except at some position where a "flipping" occurs where the eyes see the wrong pairs. This occurs at the transition from the left most to right most view (green to blue transition below). This effect is minimised by using a large number of subimages with a small angle between them. Unfortunately the number of images is constrained by the achievable resolution of the image and barrier screen. The flipping can also be reduced by maintaining a shallow depth of view.

One of the constraints with barrier methods is that so much of the image is occluded that they typically need to be printed onto a transparent sheet and back lit. They are usually mounted in special light boxes/frames. An advantage is that the image and barrier sheet can be created through the same printing process resulting is a matched image and barrier thus reducing many of the distortion effects that plague lenticular sheets.

"Lenticule" is a synonym for "lens" but has come to mean a sheet of long thin lenses. Lenticular sheets contain a series of cylindrical lenses molded into a plastic substrate. The lens focuses on an image on the back side of the lenticular sheet. The lenticular image is designed so that each eye's line of sight is focused onto different strips. The image placed behind the lenticular sheet is formed in essentially the same way as for a parallax panoramagram.

The key to successful creation of autostereoscopic images based upon lenticular sheets is the quality and uniformity of the lens. The sheet is usually made so that the back side of the sheet is exactly one focal length behind the lens so that the image data emerges collimated from each individual lens. Unlike the barrier methods, the whole surface of the lenticular sheet radiates light, there are no opaque slits.

Creating the composite image from the subimages

The way the individual images are interleaved to form a composite lenticular image has already been outlined. The general case is illustrated below for N subimages that are interleaved to form a composite that is N times wider than the individual images. Note: it is assumed that the N subimages are all the same size and correctly registered. The final image is stretched vertically so as to form a lenticular image than is of the same proportions as the subimages but N time larger (vertically a well as horizontally).

It should be noted that the final stretching could be performed just before printing, that is, the vertically stretched version need not be saved. This is a worthwhile consideration given that composite images tend to be very large and that run length encoding normally runs horizontally and thus the vertical redundancy won't be compressed. Of course one could use run length encoding on a rotated version of the lenticular composite. Note also that the image must not be compressed with a lossy compression scheme.

Creating the subimage from a 3D model

For all these techniques any set of subimages can be used. They might be images arranged as an animation sequence or indeed they could be totally unrelated images. These give rise to the lenticular special effect cards often used for advertising. The discussion here will be on creating autostereoscopic lenticular images from virtual 3D geometry, the earlier discussion is enough to form lenticular sheets of animated or arbitrary subimages. The creation of lenticular sheets from real photography will not be discussed although the technique is the same but it requires sophisticated camera mounting hardware.

Creating the N subimages from a computer based 3D model and rendering package only requires precise positioning of the camera and frustum. In the same way as there are two ways to create stereopairs, toe-in and offaxis, the same applies to creating the series of images for lenticular displays. The toe in method illustrated below rotates the camera around a single point and symmetric camera frustums are used. This is not the correct method although it does work but with distortion, namely vertical parallax.

The correct approach is to offset the camera along a linear path, ideally this involves using a offaxis frustum although a symmetric frustum can be used but the image need to be trimmed appropriately in order to line up correctly.