## 1 Introduction  
Depth estimation from Holoscopic images is a promising technique that has gained attention recently due to its advantage of calculating depth using a single-aperture camera. Holoscopic cameras are based on the same fundamental principles as conventional cameras but with an additional array of micro-lenses (MLA) in front of the image sensor. In traditional cameras, the main lens translates the object plane into the camera's image plane. The micro-lenses focus light beams from various directions onto a single pixel, thereby capturing the scene in three dimensions. The pixels behind each micro-lens record the same data as traditional cameras but with a greater precision by measuring information from different angles, as shown in Figure 1. The images formed behind each micro-lens, known as the Elemental Images (EIs), represent unique angles of light incidence. Thus, by analysing the EIs, the location and orientation of each light beam can be determined on a pixel-by-pixel basis. A sub-aperture image of a scene, or a Viewpoint Image (VPI), is created by re-sampling pixels from the same locations across the EIs. The EIs provide angular information, whereas VPIs provide spatial information. Traditionally, disparity estimation is performed on VPIs, which encompass the entire scene from a certain perspective, whereas EIs only include a portion of it. VPIs share visual characteristics with 2D orthographic stereo images, allowing existing stereo-image-based disparity estimation methods to be applied with few adjustments. Additionally, VPIs can be up-sampled using super-resolution methods [1]. However, extracting VPIs requires mapping the information gathered from the sensor to reconstruct the scene, which is not always straightforward and can sometimes lead to strong aliasing artefacts [2; 3; 4]. Lens error correction and camera calibration must firstly be performed to avoid artefacts. The geometry of the scene must also be considered during VPI creation to avoid image artefacts in areas not 'in focus' [5]. Additionally, some microlens array designs feature multiple micro-lens sizes with different focal lengths, making it impractical to extract pixels from the same location across all EIs. The convergence of light rays from multiple VPIs might result in overlapping on the image sensor, complicating the separation and extraction of individual rays. Therefore, selecting a 'patch' of pixels from each EI might be more effective in increasing the resolution and reducing the artefacts. However, it is more challenging than choosing a single pixel as these patches depend on the depth level within the scene; thus, using the same patch size throughout the entire scene could result in a distorted VPI. For instance, the ideal patch size for displaying the foreground can be excessively large for the background, leading to the occurrence of artefacts in the background. Extracting VPIs from Holoscopic images is time-consuming and requires significant storage due to the large number of VPIs generated. Estimating depth from video frames or in real-time scenarios is particularly challenging due to the large number of frames [6]. For these reasons, EIs provide a more straightforward method for estimating disparities, requiring only lens correction as a pre-processing step. In this paper, disparity estimation using perspective EIs is employed, contrary to conventional methods that use extracted, corrected, and up-sampled VPIs. Perspective projection and orthographic projection are two types of 3D projection. As seen in Figure 2, perspective projection is comparable to the human visual system, in which parallel lines in an image appear to converge at a single point; the closer the object is to the point of convergence, the smaller it appears (change in scale). Orthographic (orthogonal to the scene) projection assumes parallel lines will continue to be parallel and disregards the scaling impact.