Light field cameras and multi-camera arrays have emerged as promising solutions for accurately estimating depth by passively capturing light information. This is possible because the 3D information of a scene is embedded in the 4-D light field geometry. Commonly, depth estimation methods extract this information relying on gradient information, heuristic-based optimisation models, or learning-based approaches. This paper focuses mainly on explicitly understanding and exploiting 4-D geometrical cues for light field depth estimation. Thus, a novel method is proposed, based on a non-learning-based optimisation approach for depth estimation that explicitly considers surface normal accuracy and occlusion regions by utilising a fully explainable 4-D geometric model of the light field. The 4-D model performs depth/disparity estimation by determining the orientations and analysing the intersections of key 2D planes in 4-D space, which are the images of 3D-space points in the 4-D light field. Experimental results show that the proposed method outperforms both learning-based and non-learning-based state-of-the-art methods in terms of surface normal angle accuracy, achieving a Median Angle Error on planar surfaces, on average, 26.3% lower than the state-of-the-art, and still being competitive with state-of-the-art methods in terms of MSE $\boldsymbol {\times } 100$ and Badpix 0.07.

This paper presents a method to improve disparity maps computed from light field images using structure tensor methods, which tend to expand the borders of the occluding objects, enlarging their silhouette. The proposed method relies on the fact that such regions of the silhouette are defined by a mismatch between the disparity map edges, computed by the structure tensor, and those of the corresponding epipolar plane images (EPI) representing the light field. The proposed silhouette improvement method determines a correspondence between EPI edges and the disparity map edges, identifying the erroneous silhouette regions. The disparity map is corrected by using neighbouring values computed with high structure tensor reliability. The achieved results show that the disparity map is improved both around object edges and overall, reducing the MSE by 47.9% in comparison with other methods also based on the structure tensor.