-To improve the performance of the conventional periodic δ-function arrays (PDFA) based computational integral imaging (CII), This paper propose a method of slice image reconstruction with controllable spatial filtering by using the correlation of PDFA with elemental images in CII. Methods- The multiple PDFAs are generated with spatial periods corresponding to object’s depths with the elemental image array (EIA). They are used to generate a set of spatially filtered-EIAs for multiple object depths. the intensity of the EIA can be represented as Eq. (1), ( ) ( ) ( ) 1 0 2 , 2 N O O O E E E O O O O O n O O O x f z P z P g x x n z f z x dx dz z f z f z d - = æ + ö = çç - - ÷÷ - è + + ø òòå . (1) Equation (1) implies that the intensity impulse response of an EIA is represented as a continuously distributed periodic function. The spatially periodic information corresponding to the targeting range of object’s depth can be extracted from an EIA by using the sifting property of convolution between periodic functions, and the equation is given by ( ) ( ) ( ) 2 1 , E E O E O R x g x s z x dz a a = - ò , (2) where α1 and α2 are the range of the depth for extracting spatially periodic information from the captured EIA and the given distance value. The later part of Eq. (2) can be given by ( ) ( ) 2 2 1 1 1 0 , 2 N O O O E O E O n O O NPf z P z P s z x dz x n dz z f z f a a a a d - = æ + ö = çç - - ÷÷ è + + ø ò ò å . (3) the results of Eqs. (2) and (3) imply that the depth information could be extracted from an EIA at the continuous or partially continuous ranges. This can be represented by ( ) ( ) ( ) ( ) 2 2 1 1 , , ... E E O E O O E O R x g x s z x dz s z x dz a b a b = - é + + ù êëò ò úû . (4) Therefore, Eq. (4) presents our controllable spatial filtering in the elemental images. Results- Figure 4 shows the spatial filtering result in the conventional method. Here, the single depth was considered as shown in Fig. 4(a). Then, the spatially filtered EIA has the only single clear object as shown in Fig. 4(b). Spatial filtering results according to required depth range from the EIA are shown in Fig. 5. Fig. 4. Spatial filtering used in the conventional method. Fig. 5. Spatial filtering used in the proposed method. Conclusions- In conclusion, a method of slice image reconstruction with controllable spatial filtering by using the correlation of PDFAs with elemental images in CII has been proposed. Since the multiple PDFAs had spatial periods correspond to object’s depths with the EIA, we could generate a set of spatially filtered-EIAs for multiple object depths. The proposed method was demonstrated for partially occluded object reconstruction experiments. Preliminary experiments reveal that our method can provide the control of depth range for spatial filtering selectively-

• Jae-Young Jang(Dept. of Optometry, Eulji University)