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P4-7 Abstract -- This paper presents a fully digital auto-focusing(FDAF) system using a priori obtained point spread function(PSF) dataset. The proposed FDAF algorithm aims at low-cost,affordable consumer’s imaging electronics free from eitheroptical or mechanical focusing parts. The proposed algorithmconsists of three steps: i) a priori estimation of a set of PSFs, ii)automatic selection of a proper PSF from the blurred inputimage, and iii) restoration the out-of-focused image by selectingthe optimal PSF from the a priori obtained dataset. Theproposed algorithm can realize low-cost, high-quality imagingsystems, such as digital still cameras, mobile camera phones, andsurveillance cameras. I. INTRODUCTIONMost digital imaging products often suffer from imagedegradation due to physical limits of focusing accuracy. Manydigital cameras adopt various auto-focusing (AF) techniquesin order to remove the out-of-focus blur [1]. General AFsystems can be classified into active and passive ones, and most commercial digital cameras adopt either one of them.While an active AF system provides accurate focusingfunction, a passive AF system with image restoration functioncan remove the out-of-focus blur without additional optical or mechanical parts.In this paper we propose a real-time implementationmethod of FDAF system using a priori estimated PSF dataset.Given the PSF dataset, the proposed algorithm removes theout-of-focus blur by selecting the optimal PSF and performingimage restoration. This research is supported by Ministry of Culture, Sports and Tourism (MCST) and Korea Culture Content Agency (KOCCA) inthe Culture Technology (CT) Research & Development Program2009, and by the Industrial Technology Development program of theMinistry of Knowledge and Economy (MKE) of Korea. II. T HE P ROPOSED F ULLY D IGITAL A UTO -F OCUSING SYSTEM Fig. 1 illustrates the block diagram of the proposed algorithm. The proposed FDAF algorithm consists of constructing a PSF dataset and the AF system based on the a priori obtained PSF dataset. A. Generation of the a PSF dataset We use a set of special pattern images acquired withdifferent focusing setups as shown in Fig. 1. In order toestimate PSF at a focal distance, we first need to develop anaccurate PSF estimation method using an edge profile sincethe measure of the edge sharpness can yield the degree-of-focus. Edges are extracted in each image by using four-directional Canny-edge-detector. We then select the set of blocks containing edges, and estimate the step response acrossthe edge for each pixel. We compute the one-dimensional(1D) step response by averaging the step responses.In order to the estimation two-dimensional (2D) PSFs usingthe corresponding 1D step response, we need severalassumptions on the PSF. We first assume that a PSF isisotropic (or circularly symmetric) and that the set of concentric circles can completely characterize the PSF asshown in Fig. 2. (0) r (1) r (2) r (3) r 2 2 i j + α 1 α − i j P Fig. 2. A PSF of radius 3 characterized by the center and three concentriccircles. r(0) represents the strength of the center point, and r(k), k=1,…,3,strengths of three concentric circles. Based on the isotropic assumption, we define the strengthof the PSF on a grid P off the concentric circles of integer radius as ( ) ( ) ,()(1)1, Pijrkrk α α = + − − (1)where k represents the greatest integer that does not exceedsthe radius, and 22 ()(), 01. rkij α α = − + < < (2)Finally, we also assume that the out-of-focused image ismodeled by convolving the PSF and the input image. A Fully Digital Auto-Focusing System Using a Priori PointSpread Function Dataset Younguk Park, Jaehwan Jeon, Jinhee Lee, and Joonki Paik Image Processing and Intelligent Systems Laboratory, Chung-Ang University, Seoul, Korea Fig. 1. Block diagram of the proposed FDAF system. 978-1-4244-4316-1/10/$25.00 ©2010 IEEE For the estimation 2D PSF we solve the following linear equations , Ars = (3)where A represents the ( ) 1 DR × + matrix whose elementhas the cumulative value of element of Fig. 2. r and s represent the (1)1 R + × vector for strength values of concentric circles and the 1 D × vector for step responses,respectively. Because the linear equation (3) has moreequations than unknowns, such as (1) DR > + , it can besolved by using singular value decomposition (SVD) [2].Given[(1),...,()] T rrrk = , we finally generate the PSFusing linear interpolation on the grid shown in Fig. 2.Finally, The 1D step responses and 2D PSF of the list of theimages will be stored in the database module and selectivelyused at the restoration stage. B. Auto-focusing based on a PSF database Given an input out-of-focused image, we can select theoptimal PSF by comparing the 1D step response with in the pre-estimated dataset. In order to detect the optimal PSFamong, 1D step response of blurred input image is estimated in the same manner of subsection A. We compare the blurred 1D step response and the pre-saved PSF dataset. Difference between two parameters is computed as 1 min[()], M i Databaseblurred i DSS = = −∑ (4)where i Database S represents the 1D step response in thedataset, M the total number of PSFs in the dataset, and blurred S the blurred 1D step response. The optimal PSF isselected with the minimum D .We finally obtain an in-focused image by using digitalimage restoration with the optimally selected PSF. For therestoration process we adopt the constrained least squares(CLS) filter because of its computational efficiency.III. E XPERIMENTAL R ESULTS In this section, we show the experimental results of the proposed FDAF system.Fig. 3.(a) shows the srcinal image of size 1366782 × . Wesynthetically made an out-of-focused image by convolvingwith 1111 × Gaussian PSF as shown in Fig. 3.(b). Thecorresponding edge classification results are shown in Fig. 3.(c). According to the proposed step response estimationalgorithms, the step response, which is orthogonal to thedirection of edge, is shown in Fig. 3.(d). Fig. 3.(e) shows a setof pattern images captured at the different distances for generating a PSF dataset. Fig. 3.(f) and Fig. 3.(g) show the 1Dstep responses and the 2D PSFs in the dataset, respectively.The selected 2D PSF is shown in Fig. 3.(h), and the restored image using the CLS restoration filter is shown in Fig. 3.(i).After confirming the performance of the proposed method using a simulated blurs, we use a real image captured by adigital camera. The input image has out-of-focused blur, asshown in Fig. 4.(a). Fig. 4.(b) shows the restored image usingthe CLS filter using the optimally selected PSF.IV. C ONCLUSION In this paper, we proposed a FDAF system based on a prioriPSF dataset. The proposed FDAF approach can beimplemented in real-time. The main advantage of the proposed algorithm is that it computes optimal PSF of blurred input image without the PSF estimation. In experimentalresults, we showed that the proposed algorithm can efficientlyremove the out-of-focus blur through the optimally selected PSF from the pre-estimated dataset. As a result it is far moreefficient than the existing methods in terms of both focusing performance and computational complexity. In addition, the proposed FDAF system has wide applications including adigital camera, a digital camcorder, and a surveillance system.(a) (b) (c) (d) (e) (f)(g) (h) (i) Fig. 3. (a) well-focused srcinal image, (b) the degraded image, (c) the edgemap computing from (b), (d) 1D step response extracting from (c), (e) regular image for database, (f) 1D step responses database, (g) 2D PSFs of databaseon (f), (h) selected PSF from (g), and (i) the restored image. (a) (b) Fig. 4. (a) out-of-focus blur image, (b) the restored image using the proposed algorithm. R EFERENCE [1] S. Kim, S. Park, and J. Paik, Simultaneous out-of-focus blur estimationand restoration for digital AF system, IEEE Trans. Consumer Electronics, vol. 44, no. 3, pp. 1071-1075, August 1998.[2] I. Bau, N. Lloyd, Numerical linear algebra , Philadelphia: Society for Industrial and Applied Mathematics, 1997.
