# All-in-Focused Image Combination in the Frequency Domain Using Light Field Images
## 1 Introduction  
Light field cameras, also called plenoptic cameras, have been popularly used in digital refocusing and three-dimensional reconstruction. They are fabricated with internal micro-lens arrays to capture light field information in such a way that one can refocus the image after acquisition. This is the very unique capability of the light field camera [1]. Due to the finite depth of field (DOF) in normal digital cameras, an image of all of the relevant objects displays sharpness information inside the DOF; however, the objects show blurred information outside the DOF. Since the light field image generates a set of images focused at different depth levels after being captured, it is suggested that one can determine objects in the foreground and background regions. Moreover, it can generate a set of multi-view images without the need for calibration images.  
All-in-focused image combination is a method for merging in-focused information of the stack images that are captured at different focal planes from the same position. This algorithm addresses a method to fuse image sequences for reconstructing the all-in-focused image so that all relevant object regions appear sharp in the final image reconstruction. For detecting in-focused regions of the images and combining them for the all-in-focused image, various methods have been studied for focus measurement using the whole images. Up to now, various focus measurement and image combination methods have been proposed for different applications. [PERSON] and [PERSON] have proposed a focus measure operator that applies flexibly shaped and weighted support windows [2]. The algorithm can retrieve the depth discontinuities. The all-focused image is used to determine the support window. [PERSON] et al. have presented a focus detection method that portions source images into edges, textures, and smooth regions [3]. Focused regions are measured by morphological components. The final fused images are combined with the fusion map. [PERSON] et al. have suggested a multi-focus image fusionmethod for visual sensor networks in the discrete cosine transform (DCT) domain [4]. This method utilizes variance values to measure and fuse multi-focus images using DCT-based algorithms. [PERSON] and [PERSON] have introduced the DOF extension using a fusion of two images [5]. Their algorithm applies the DCT-STD and the DWT-STD for focus detection. Besides that, [PERSON] et al. have demonstrated a multi-spectral imaging method that can also show the color image reproduction [6; 7; 8].  
While most previous methods for image combination employed a few inputs of different focal images, we attempt a new method for image composition using many input images. In this paper, we describe a new all-in-focused image combination method that integrates the sum of updated modified Laplacian (SUML) and the harmonic mean (HM) in the discrete cosine transform (DCT) domain.  
The sum of modified Laplacian (SML) performs better than other focus criteria [9] and HM is more robust than the arithmetic mean because they both support small pieces of information and increase their influences on the overall estimation operation. Moreover, the proposed method takes advantages of image representation in the frequency domain. Since it is difficult to classify in-focused and out-focused regions in the spatial domain when edges of the out-focused parts are sharp, we transform images into the frequency domain to analyze the image information. The main contributions of this paper are: (1) The method for extending the DOF in the imaging system that creates an image from a set of different focal images at one shot capture, and (2) the effective method for all-in-focused image combination that is performed in the frequency domain to avoid the artifacts reduction process in the spatial domain that requires a complexity execution.