# Optimal View Estimation Algorithm and Evaluation with Deviation Angle Analysis
## 1 Introduction  
Viewpoint estimation and analysis have been popular and important subjects in computer vision, three-dimensional (3D) scene understanding [1, 2], object detection and image analysis [3], and so on. According to different application data and research purposes, viewpoint estimation problems can be roughly divided into two categories: 3D model-based viewpoint estimation and image-based viewpoint estimation. The 3D model-based viewpoint estimation method aims to find the best view of a 3D model which serves as the input data. The best view can be defined based on requirements from geometric shape features to aesthetic needs. In 2012, [PERSON] et al. [4] presented three best view selection approaches: (1) based on geometry and using the maximum amount of visible vertices, (2) employing the visual attention model, and (3) calculating the amount of information in a scene after projecting the 3D model to the 2D image using entropy. In 2004, [PERSON] et al. [5] found that textures constructed from planes more nearly orthogonal to the line of sight tend to be better at revealing surface shape, and that viewing surfaces from an oblique view is significantly more effective for revealing surface shape than viewing them from directly above. For bas-relief generation and synthesis, [PERSON] et al. [6] divided this problem into two parts: selecting the best view and arranging the relief layout. In 2020, [PERSON] et al. [7] projected a 3D shape onto its best-view images to develop a 3D shape retrieval system. From another perspective, the problem of selecting the best view is mainly considered a task of capturing the most information about the 3D shape, which is highly intuitive and closely related to human perception. In 2011, [PERSON] et al. [8] proposed an approach to automatically select the best view for a 3D shape by internet image voting (IIV), assuming that in a network of similar object images, the viewpoint with the highest number of images from the same viewpoint reflects the aesthetic preferences of the public. In addition, in 2021, [PERSON] et al. [9] introduced a reinforcement learning approach utilizing a novel topology-based information gain metric to determine the next best view of a noisy 3D sensor. The image-based viewpoint estimation method aims to find the viewpoint at which the camera captures the input image. In 2016, [PERSON] et al. [10] estimated a 3D human pose from a single RGB image. For the problem of selecting the optimal viewpoint for taking good photographs for architecture, [PERSON] et al. [11] addressed this by learning from professional photographs of world-famous landmarks available on the internet. In addition, viewpoint estimation can be used to construct a depth map of an image [12]. In 2020, [PERSON] et al. [13] used a specially designed GAN model to map a given natural image to a geometry image, from which the corresponding 3D mesh can be reconstructed with accurate viewpoint information. Given that viewpoint estimation from 2D-rendered images helps understand how users select viewpoints for 3D model (point cloud, mesh, or voxel) visualization and guides users to select better viewpoints based on previous visualizations [14], this paper focuses on this topic, i.e., image-based viewpoint estimation. To evaluate the accuracy of the image-based viewpoint estimation method, it is generally necessary to have images with known viewpoints. This type of data is paired data of images and corresponding viewpoint labels, which can be generated using the 3D model-based method by projecting to a plane specified by the viewpoint. As is well known, training deep neural networks to estimate the viewpoint of objects requires large labeled training datasets [15]. Therefore, building such a dataset is a valuable task. Traditionally, based on such a dataset, the accuracy of viewpoint estimation can be calculated by the deviation and cosine distance to measure the error.