Sub-aperture


Similar to an array of cameras, the Standard Plenoptic Camera allows for a multiview image acquisition. However, in contrast to a camera array, a plenoptic camera requires an additional image processing procedure to extract these so called sub-aperture images (multiview images). As seen in the animation below, each micro image position u is highlighted by a colour representing a sub-aperture. Further details on the triangulation, baseline and tilt angle can be found below.


Sub-aperture using the ray tracing intersection model

According to the suggested model, the extraction procedure selects all pixels sharing the same relative position u, i.e. same colour, under each micro lens and places them in a new image whereas each selected pixel is rearranged based on its dedicated micro lens position s. For instance, the central position u1, highlighted in yellow color, corresponds to the central view and surrounding positions u, e.g. blue or green, represent adjacent views from different perspective. Accordingly, the extraction process implies that the number of sub-aperture views amounts to the micro image resolution and the effective resolution of a sub-aperture image equals the number of micro lenses in the plenoptic camera it has been captured with. Below you can find an alternative scheme illustrating the rearrangement of pixels in the sub-aperture extraction process.



Sub-aperture Extraction


Triangulation


In stereoscopy and multi-view camera systems, it is well studied in which way the cameras' positions affect a depth map's quality. The key parameter in stereoscopic vision is the 'baseline', a technical term used to describe the distance separating optical centres of two objective lenses from each other. Although real camera positions are easy to measure in traditional stereoscopy, it is not obvious how to determine the baseline and tilt angle in a Standard Plenoptic Camera. For example, baseline and tilt angle parameters are needed when screening light field camera content on autostereoscopic displays. Besides, it would be interesting to see the impact of the plenoptic lens design on the acquired depth information. Based on the provided Standard Plenoptic Camera Model, explanations below answer these questions.



Baseline

Baseline using the ray tracing intersection model

Examination of the proposed suggests that tracing the paths from light field rays in object space yields intersections along the entrance pupil A''. Since all chief rays, that form a sub-aperture light beam, travel through the same point A''i, this point can be regarded as the optical centre of a virtual camera lens. Accordingly, a virtual optical centre A''i is given by calculating slopes of respective object rays and finding their intersection along the entrance pupil. Similar to stereoscopic imaging, baselines BG in the Standard Plenoptic Camera can then be obtained by the distance of two virtual optical centres such that BG = A''i + A''i+G .



Tilt angle

If each sub-aperture light beam (highlighted with colours) belongs to a virtual camera lens A''i, its chief ray z'i can be thought to be its optical axis. An optical axes z'i may be used to indicate the tilt angle of each virtual camera lens. As depicted in the figure below, by shifting the main lens along zU, we observe that optical axes z'i change their slope with respect to zU except for the central optical axis z'0. Therefore, this behaviour can be seen as tilting the virtual camera lenses. Detailed information on the mathematical geometry can be found in the publication list.



Related Publications



Baseline and triangulation geometry in a standard plenoptic camera   

C. Hahne, A. Aggoun, and V. Velisavljevic, S. Fiebig, and M. Pesch "Baseline and triangulation geometry in a standard plenoptic camera," Int. J. of Comput. Vis. (IJCV), (2017).

[PDF] [BibTeX]


Light field geometry of a standard plenoptic camera

C. Hahne, A. Aggoun, S. Haxha, V. Velisavljevic, and J. Fernández, "Light field geometry of a standard plenoptic camera," Opt. Express 22, 26659-26673 (2014).

[PDF] [BibTex]


Baseline of virtual cameras acquired by a standard plenoptic camera setup

C. Hahne, A. Aggoun, S. Haxha, V. Velisavljevic, and J. Fernández, "Baseline of virtual cameras acquired by a standard plenoptic camera setup," in 3D-TV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 2-4 July 2014.

[PDF] [BibTex]


Embedded FIR filter design for real-time refocusing using a standard plenoptic video camera   [Invited paper]

C. Hahne and A. Aggoun, "Embedded FIR filter design for real-time refocusing using a standard plenoptic video camera," Proc. SPIE 9023, in Digital Photography X, 902305 (March 7, 2014).

[PDF] [BibTex]



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