###### Abstract  
This paper presents a new method for extracting an elemental image array in three-dimensional (3D) integral imaging. To reconstruct 3D images in integral imaging, as the first step, a method is required to accurately extract an elemental image array from a raw captured image. Thus, several methods have been discussed to extract an elemental image array. However, the accuracy is sometimes degraded due to inaccurate edge detection, image distortions, optical misalignment, and so on. Especially, small pixel errors can deteriorate the performance of an integral imaging system with a lens array. To overcome the problem, we propose a postprocessing method for the accurate extraction of an elemental image array. Our method is a unified version of an existing method and proposed postprocessing techniques. The proposed postprocessing consists of re-calibration and lens array area detection. Our method reuses the results from an existing method, and it then improves the results via the proposed postprocessing techniques. To evaluate the proposed method, we perform optical experiments for 3D objects and provide the resulting images. The experimental results indicate that the proposed postprocessing techniques improve an existing method for extracting an elemental image array in integral imaging. Therefore, we expect the proposed techniques to be applied to various applications of integral imaging systems  
three-dimensional integral imaging; elemental image array (EIA); lens array; lattice detection; calibration 202212925202220222022  
In integral imaging, the setup of a pick-up process consists of a lens array and a capturing device such as a camera, as shown in Figure 1a. The process converts a raw image from a capturing device into an elemental image array (EIA). To reconstruct 3D images effectively and to improve the accuracy of the reconstruction, the process requires an accurate method to extract elemental images without distortion or loss of data. Thus, various methods to extract an elemental image array in 3D integral imaging have been discussed [24; 25; 26; 27; 28; 29; 30]. Among them, a technique using projection profiles was introduced to extract the two-dimensional (2D) lattice line structure, where the boundaries of the element images are estimated through projection profiles [24; 25]. A projective transformation was applied to reduce errors by correcting the perspective distortion [26]. Moreover, a calibration pattern image was addressed to extract an elemental image array [27]. To increase the robustness of detecting the lens array lattice, a line segment detection algorithm was studied [28]. In addition, some methods using markers attached to the surface of a lens array were discussed to detect an elemental image array [29; 30]. These existing methods can extract an elemental image array from a raw image of a lens array. However, the methods can suffer from inaccurate edge detection, image distortions, and optical misalignment, thus the performance of extracting elemental images can be degraded. Especially, the lens distortion or the inaccurate edge detection likely occurs on the boundaries of each lens within EIA. In this case, the size and location of each elemental image are inaccurate. Therefore, a study is still required for improving the accuracy of extracting elemental images. In this paper, we propose a postprocessing method to accurately extract an elemental image array in 3D integral imaging. The proposed method improves the accuracy of an existing method by use of re-calibrating the results of the existing method. The proposed re-calibration algorithm calibrates the size and location of each elemental image by estimating the number of lenses accurately. In addition, we propose an algorithm to detect the lens array area via reusing intermediate data of an existing method. Thus, the extraction performance of an existing method can be improved by adding the proposed postprocessing techniques. To evaluate the proposed method, optical experiments are conducted.