# Pose Estimation of Primitive-Shaped Objects from a Depth Image Using Superquadric Representation  
[PERSON]  
1 Department of Information and Computer Science, Keio University, Yokohama 223-8522, Japan; [EMAIL_ADDRESS]  
20 June 2020003 August 20  
a cuboid, two parameters (height and radius) exist to represent a cylinder, and one parameter (radius) exists to represent a sphere. These parameters can be estimated by setting the cost function against each primitive shape representation. However, these methods for primitive shape pose estimation explicitly use limited kinds of shape representation, which also limits the application of the pose estimation of primitive-shaped objects. Superquadric is one of an ideal shape representation for adapting various kinds of shapes using a single equation [12]. Applying the superquadric to an object enables the object to be expressed by various primitive shapes--such as cuboids, cylinders, and spheres--with several parameters in the equation. As we aim to estimate the pose of geometrically simple objects, we assume that the objects can be represented by superquadrics. A naive approach to estimating the pose of objects that are represented by superquadrics is to apply the method proposed by [PERSON] et al. [13]. They proposed a method to estimate the superquadric parameters and 6 DoF pose parameters from the 3D point cloud of the object. After extracting the 3D point cloud of the object from the depth image, superquadric and pose parameters can be estimated using their method. However, the superquadric parameter estimation methods takes the input of the 3D point cloud of the object at the optimization, thereby requiring the segmentation against the obtained depth image the result of parameter estimation also relies on the quality of depth image segmentation. That is, if the object point clouds have outlier points that are caused by miss-segmentation, the parameters that fit the outliers are estimated, and these points would lead to a low accuracy of the pose estimation. In order to achieve a robust superquadric pose estimation, it is important to exclude the 3D points that are not 3D points of the objects. One simple idea to exclude the outlier point is to employ the threshold value to cut off those points that are further from the object centroid. However, the threshold value differs among objects in accordance with their scale and shape, thereby defining the threshold hyper parameter against each object. Therefore, we introduce the coefficient that implicitly down-weighs outlier points and is invariant to the shape and scale of objects. In this paper, we present a method for estimating the 6 DoF pose of primitive-shaped objects from sequential depth images. In order to estimate the pose parameters, we propose the novel pose prediction method of primitive-shaped objects using superquadric representation that is robust to outliers and irrelevant to the shape or scale of the object. The results of the proposed method is shown in Figure 1. At the initial frame, we geometrically segment the depth image using normal vector concavities and depth continuities. Second, we label the binary segmented depth image by using the connected component algorithm. Thereafter, we estimate the superquadric shape, scale, and pose parameters to the each primitive-shaped object. In successive frames, we match the label map at the initial frame and the current frame to find the object, and we update the pose parameter of each primitive-shaped object. As our method enables us to estimate the pose of superquadrics even if the outlier points exist in the object point cloud, our method can handle a case in which a person freely moves objects. In such a case, miss-segmentation can occur easily. In the experiment, we captured four scenes in which the user interacts with four primitive-shaped objects to show the robustness of our proposed method. We compare the pose estimation results with two baseline methods.