PointCNN is a novel framework for learning features from point clouds, which generalizes traditional convolutional neural networks (CNNs) to handle irregular and unordered data. The key idea is to apply a transformation called X-Conv, which first transforms the input points and their features, then applies a typical convolution. This approach addresses the challenges of directly applying convolutions on point clouds, such as losing shape information and being sensitive to point ordering. The X-Conv operator learns to weight and permute the input features, enabling the convolution to be invariant to point ordering while preserving shape information. The X-Conv process involves transforming the coordinates of input points into a local coordinate system, lifting these coordinates into a higher-dimensional space, and combining them with the associated features. This allows the convolution to operate on a more structured representation of the data. The X-Conv operator is then applied to the transformed features, resulting in a more robust and effective feature learning process. PointCNN is designed to handle both classification and segmentation tasks on point cloud data. It uses hierarchical convolutions to progressively reduce the number of points while increasing the richness of their features. This hierarchical structure allows the model to capture increasingly complex patterns in the data. The model is also capable of handling point clouds with or without additional features, making it versatile for various applications. Experiments show that PointCNN achieves performance comparable or better than state-of-the-art methods on multiple benchmark datasets, including ModelNet40, ScanNet, and ShapeNet Parts. It outperforms other methods in tasks such as 3D shape segmentation and classification. Additionally, PointCNN is effective in processing sketches and other irregular data, demonstrating its versatility and robustness. The X-Conv operator is differentiable, allowing it to be integrated into a neural network for training. The model is implemented using standard deep learning frameworks and has been tested on various datasets, showing its effectiveness in learning meaningful features from point clouds. The use of X-Conv enables PointCNN to handle the challenges of point cloud data while maintaining the power and flexibility of traditional CNNs.PointCNN is a novel framework for learning features from point clouds, which generalizes traditional convolutional neural networks (CNNs) to handle irregular and unordered data. The key idea is to apply a transformation called X-Conv, which first transforms the input points and their features, then applies a typical convolution. This approach addresses the challenges of directly applying convolutions on point clouds, such as losing shape information and being sensitive to point ordering. The X-Conv operator learns to weight and permute the input features, enabling the convolution to be invariant to point ordering while preserving shape information. The X-Conv process involves transforming the coordinates of input points into a local coordinate system, lifting these coordinates into a higher-dimensional space, and combining them with the associated features. This allows the convolution to operate on a more structured representation of the data. The X-Conv operator is then applied to the transformed features, resulting in a more robust and effective feature learning process. PointCNN is designed to handle both classification and segmentation tasks on point cloud data. It uses hierarchical convolutions to progressively reduce the number of points while increasing the richness of their features. This hierarchical structure allows the model to capture increasingly complex patterns in the data. The model is also capable of handling point clouds with or without additional features, making it versatile for various applications. Experiments show that PointCNN achieves performance comparable or better than state-of-the-art methods on multiple benchmark datasets, including ModelNet40, ScanNet, and ShapeNet Parts. It outperforms other methods in tasks such as 3D shape segmentation and classification. Additionally, PointCNN is effective in processing sketches and other irregular data, demonstrating its versatility and robustness. The X-Conv operator is differentiable, allowing it to be integrated into a neural network for training. The model is implemented using standard deep learning frameworks and has been tested on various datasets, showing its effectiveness in learning meaningful features from point clouds. The use of X-Conv enables PointCNN to handle the challenges of point cloud data while maintaining the power and flexibility of traditional CNNs.