# Animal Pose Estimation Based on 3D Priors
## 4 Proposed Method
### Pose Refinement
#### 4.3.1 Optimization-Based Pose Refinement
The 2D input vectors are connected to a fully connected layer to expand the dimensionality to 1024 and then fed into subsequent residual blocks. Afterward, the network splits into two paths that predict the coefficients and the rotation matrices. Each path has two consecutive residual blocks followed by a fully connected layer that downscales the features to the required scale. ## 5 Experiments

We evaluate the effectiveness of the proposed method in this section. As a pose refinement module, the proposed method can be regarded as the postprocessing of existing pose estimation algorithms. Therefore, we applied the proposed method to state-of-the-art pose estimation methods and evaluated its effectiveness on different datasets. Figure 5: Overview. Given the initial pose \(p\), the coefficient network and camera network estimate coefficients \(c_{k}\) and rotation matrix \(R_{k}\) in Equation (6), respectively. The coefficients \(c_{k}\) and the rotation matrix \(R_{k}\) are combined with the 3D pose dictionary \(B\) to generate a 3D pose corresponding to the initial pose \(p\). The 3D pose \(P\) is reprojected to obtain the refined pose \(p^{\prime}\). ### Datasets

Synthetic animal. The synthetic animal dataset in [15] consists of images of elephants, horses, hounds, sheep, and tigers. In this dataset, animal textures and backgrounds are randomly synthesized using the COCO dataset [54]. For each animal species, 5000 images were generated with random textures and 5000 images with textures derived from the original CAD model. We only used the tiger subset, denoted by SA-Tiger, in our experiments (see Figure 6a). TigDog. The TigDog dataset [55] provided key-point annotations for horses and tigers, where the images were taken from YouTube (for horses) and National Geographic documentaries (for tigers). Each image was annotated with 19 key points. These key points were distributed as follows: two key points on the eyes, one key point on the chin, two key points on the shoulders, twelve key points on the legs, one key point on the hip, and one key point on the neck. Among them, 11 key points overlapped with those defined by the ATRW [24]. These overlapping key points were used for evaluation in this paper. For convenience, we call the subset of tiger images in this dataset TD-Tiger (see Figure 6b). Amur. As described in Section 3.2, Amur is a tiger image dataset. The image quality in this dataset is poor due to factors such as complex backgrounds, unconstrained illumination, and four-limbed movement. We manually annotated these samples for experimental evaluation (see Figure 6c). ### Experimental Setup

As in [56], we used the percentage of correctly localized key points (PCK) as the metric for evaluation. For the \(i\)-th sample in the test set, PCK defines the predicted position of the \(j\)-th key point, \(\hat{y}_{i}^{j}\), which would be correct if it falls within a threshold of its ground-truth position \(y_{i}^{j}\). \[\left\|y_{i}^{j}-\hat{y}_{i}^{j}\right\|_{2}\leq\beta\mathcal{D} \tag{10}\]

where \(\mathcal{D}\) is the reference normalizer, namely the maximum side length of the image bounding box for animals, and \(\beta\) controls the threshold for correctness. \(\beta\) was set to 0.05 as in [56]. ### Results on the SA-Tiger Dataset

In order to analyze the robustness of the proposed method to noise, we added noise to ground truth, just as [57]. The corrupted dataset was then used to evaluate the performance of the proposed 3D constraints in correcting the corrupted 2D poses. As in [57], we estimate the scale \(s\) by finding the maximal length of the bounding box along \(x,y-axis\). Then, we sampled zero-mean Gaussian noise with standard variance \(\sigma=\delta\%\times s\), where \(\delta\) were set to 3, 4, 5, and 6. The SA-Tiger dataset had 10,000 samples, which were randomly divided into 6000 training samples and 4000 testing samples. We trained the neural networks in both fully supervised and self-supervised ways. Fully Supervised: The initial pose \(p\) was used as the network input.