Multi-View Omni-Directional Imaging

Transcription

1 Multi-View Omni-Directional Imaging Tuesday, December 19, 2000 Moshe Ben-Ezra, Shmuel Peleg Abstract This paper describes a novel camera design or the creation o multiple panoramic images, such that each location in the scene may be viewed rom dierent viewpoints in dierent images. The resulting images can be viewed by a human observer, creating depth and motion sensation. The new camera can create images with a ield o view o up to a ull 360 o, and can have viewpoints rom a range o possible viewpoints. The resulting images can be captured by photographic material or by an electronic sensor. The resulting images can be viewed by a multiple-view display such as a lenticular array, or by a stereopair display such as a stereo Head Mounted Display. Viewing with a Head Mounted Display enables the application o Automatic Disparity Control. A similar setup can be used to photograph an object rom the outside towards the inside, creating a stereo view o the object rom all directions around the object. 1

2 1. Introduction A pinhole camera is the most common camera model characterized by having a single center o projection (the pinhole). Some applications like stereo panorama require multiple center o projection such as the circular projection model [1]. This document describes a new camera model, a Dual Slit Camera model, and its application or multi-view omni-directional photography. 2. The dual slit camera Model First slit Second slit Image plane p=(x,y) P=(X,Y,Z) (0,0) + Z 1 2 Figure 1: Dual Slit Camera Model Figure 1 describes the dual slit camera model: A camera having two ininitesimally narrow linear slits between the scene and the image plane. A scene point P=(X,Y,Z) is visible on the image plane at location p=(x,y). The point P and the First slit deine a plane B 1 in 3D (not shown). The same point P and the second slit deine a second plane B 2 in 3D (not shown). When the two slits are not in the same plane, the two planes B 1 and B 2 intersect with the image plane at a point p(x,y) which is the projection o P(X,Y,Z). 2

3 Simple geometry shows that Point P = (X,Y,Z) in the scene is projected with this model into point p= X Z 1, 1 Y Z 2 2 in the image plane. This setup is a generalization o the pinhole camera model, since when ( 1 = 2 ), the two slits touch, and their intersection orms a pinhole. The resulting images thereore vary rom regular pinhole camera images to a small vertical strip images in the case that the second slit is ar rom the irst one and is close to the image plane. The two slits projection has three stages: 1. A projection rom a point to a plane by the irst slit. 2. A projection rom a plane to a line by the second slit. 3. Intersection o the line with the image plane to orm a point. This separation enables several generalizations, among them: 1. Have a single slit at the irst stage, and multiple slits at the second stage. The multiple slits are arranges so that the image behind each slit does not overlap the images behind other slits. The image behind each slit has one horizontal viewpoint deined by the second slit, and one vertical viewpoint deined by the irst slit. This arrangement thereore creates many images, one behind each o the second slits, each having a dierent horizontal view o the scene. 2. Enable the irst stage to cover a complete 360 0, which is possible or a slit that is a horizontal circle. Implementation: In practice the system, like all cameras, will be implemented in optics using lens. Each slit can be approximated by a 3

4 cylindrical lens. The multiple second slits can be implemented by an array o cylindrical lens, also called a lenticular lens. 3. Multi-view image ormation P Q a b c P Q P Q Fig 2 Image Formation Figure 2 describes the multi-view image ormation or two points P and Q and or two rays or each point. a is a horizontal ront slit (or its implementation with cylindrical lens), b is a lenticular array, representing the 2 nd array o vertical slits, c is the sensor plane either chemical or electro-optical sensor. We can see that P and Q are projected into dierent locations over the sensor plane creating a multiple view image. 4

5 Now, Consider P and Q to be the eye s o an observer looking at the image at sensor plane. Each eye sees exactly all the rays that go though P and Q respectively (dashed lined) - thereore each eye sees a perspective projection image as i a pinhole camera took it, moreover, they can move horizontally within the viewing angle o each cylindrical lens giving a sense o parallax motion in addition to stereo. 3. Camera setup or stereo panorama imaging a b Fig 2 stereo panorama camera Figure 2 describes the stereo panorama camera layout. a is the irst slit or cylindrical lens which is now the shape o a torus. B is the lenticular array acing a, with the sensor attached to it at the inner layer. 5

6 5. Camera setup or 3D Object imaging b a 3D object Imaging The object is located inside the camera, a is the irst slit, b is the lenticular array acing the object and the sensor plane at the outer layer. When viewing, the cylinder should be revered so the lenticular array will ace the viewer. It is possible that the image should be lipped as well. This setup orms a cheap easy to photograph approximation o a hologram (although the technique is dierent). Reerences [1] Peleg, S., Ben-Ezra, M. Stereo Panorama with a Single Camera, CVPR99(I: ). 6