Coded Lens: Using Coded Aperture for Low

Coded Lens: Using Coded Aperture for Low
Coded Lens: Using Coded Aperture for Low-cost and Versatile Imaging
Yusuke Sekikawa, Sang-won Leigh, Koichiro Suzuki
MIT Media Lab, DENSO IT Laboratory⇤
Figure 1: (a) Prototype, (b) Image formation model, (c) Real scene reconstruction, (d) Adjusting focus
Abstract
We propose Coded Lens, a novel system for lensless photography.
The system does not require highly calibrated optics, but instead,
utilizes a coded aperture for guiding lights. Compressed sensing
(CS) is used to reconstruct scene from the raw image obtained
through the coded aperture. Experimenting with synthetic and real
scenes, we show the applicability of the technique and also demonstrate additional functionality such as changing focus programmatically. We believe this will lead to a more compact, cheaper and
even versatile imaging systems.
1
Introduction
Optical lenses are critical overhead for digital cameras, mainly due
to its size and high price. Pinhole cameras bypass this problem.
However, they have extremely slow shutter speed making them
unsuitable for handheld photography, and provide no control over
imaging parameters e.g. focus, aperture size.
A good solution for this is to use multiple pinholes for collecting
more lights. From that idea, researchers started exploring the possibility of using coded aperture for X-Ray systems, however, they required additional light-guiding hardware (e.g. collimator) to make
perfectly controlled imaging condition [Busboom et al. 1997]. In
this paper, we propose a coded aperture imaging technique using
CS without need of the lens or light-guiding hardware. It not only
provides more compact and affordable optics system, but also the
function of digitally focusing image after the picture is taken as in
[Veeraraghavan et al. 2007], but without any optical lens.
2
Proposed method
The proposed system is illustrated in Figure 1. It has a layer of
coded aperture standing in front of CMOS sensor, which makes the
observed image (by the sensor) be convolution of multiple pinhole
images projected through each pixel in the aperture. And due to its
⇤ {sekikawa,sangwon}@mit.edu,
[email protected]
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SIGGRAPH 2014, August 10 – 14, 2014, Vancouver, British Columbia, Canada.
2014 Copyright held by the Owner/Author.
ACM 978-1-4503-2958-3/14/08
finite size, the CMOS sensor crops the observed image. We define
this observation process using matrix A, which is dependent on the
desired focus f ,
(1)
y = A (f ) s = Cf (s ? p (f ))
where p (f ) is the aperture’s point spread function (PSF) and Cf
is cropping function, both dependent on focus parameter f . Our
goal is to reconstruct the scene s from the observation y with the
aperture pattern and the desired focus f given. However, the convolution and the cropping make the observation incomplete, and
therefore, making the reconstruction difficult.
CS theory provides good strategy dealing with such missing observation problem. If the scene s can be regarded as a sparse signal x
in some basis , the scene s can be reconstructed from incomplete
observation y
min ↵ · TV (s) +
· | s|l1 , s.t. A (f )
1
x=y
(2)
where TV is total variation function (TV) for smoothness constraint, and ↵, are weight for TV and L1 term. However, because A is a large matrix, it is impractical to use equation (1)
for this optimization. For this, we can rewrite equation (1) as
y = Cf (i↵t2 (D (p (f )) ⌦ ↵t2 (s)) where, D is Optical Transfer Function (OTF) [Yin et al. 2010]. This makes the computation
reasonably efficient.
3
Experiment
We used Sony Alpha7 camera (24 mega pixels 14bit RGB) with a
aperture pattern mask (size of 23.9mm square, and 0.188mm per
each pixel). Initial reconstruction was obtained using L-2 minimization with Sparse Equations and Least Squares algorithm, and
then the result was optimized through CS framewrok. Results are
shown in Figure 1 - (c) shows a successful reconstruction of a indoor scene, and (d) demonstrates computationally adjusting the distance of focal plane by changing matrix A.
References
B USBOOM , A., S CHOTTEN , H. D., AND E LDERS -B OLL , H. 1997. Coded aperture
imaging with multiple measurements. J. Opt. Soc. Am. A.
V EERARAGHAVAN , A., R ASKAR , R., AGRAWAL , A., M OHAN , A., AND T UMBLIN ,
J. 2007. Dappled photography: Mask enhanced cameras for heterodyned light
fields and coded aperture refocusing. In ACM SIGGRAPH 2007 Papers.
Y IN , W., M ORGAN , S., YANG , J., AND Z HANG , Y. 2010. Practical compressive
sensing with toeplitz and circulant matrices. In Visual Communications and Image
Processing 2010.
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