Processing blurred images is a key problem in many image applications. Existing methods to obtain blur invariants which are invariant with respect to centrally symmetric blur are based on geometric moments or complex moments. In this paper, we propose a new method to construct a set of blur invariants using the orthogonal Legendre moments. Some important properties of Legendre moments for the blurred image are presented and proved. The performance of the proposed descriptors is evaluated with various point-spread functions and different image noises. The comparison of the present approach with previous methods in terms of pattern recognition accuracy is also provided. The experimental results show that the proposed descriptors are more robust to noise and have better discriminative power than the methods based on geometric or complex moments.

Discrete orthogonal moments have been recently introduced in the field of image analysis. It was shown that they have better image representation capability than the continuous orthogonal moments. One problem concerning the use of moments as feature descriptors is the high computational cost, which may limit their application to the problems where the online computation is required. In this paper, we present a new approach for fast computation of the 2-D Tchebichef moments. By deriving some properties of Tchebichef polynomials, and using the image block representation for binary images and intensity slice representation for grayscale images, a fast algorithm is proposed for computing the moments of binary and grayscale images. The theoretical analysis shows that the computational complexity of the proposed method depends upon the number of blocks of the image, thus, it can speed up the computational efficiency as far as the number of blocks is smaller than the image size.

Background: Renal cancer is one of the 10 most common cancers in human beings. The laparoscopic partial nephrectomy (LPN) is an effective way to treat renal cancer. Localization and delineation of the renal tumor from pre-operative CT Angiography (CTA) is an important step for LPN surgery planning. Recently, with the development of the technique of deep learning, deep neural networks can be trained to provide accurate pixel-wise renal tumor segmentation in CTA images. However, constructing the training dataset with a large amount of pixel-wise annotations is a time-consuming task for the radiologists. Therefore, weakly-supervised approaches attract more interest in research. Methods: In this paper, we proposed a novel weakly-supervised convolutional neural network (CNN) for renal tumor segmentation. A three-stage framework was introduced to train the CNN with the weak annotations of renal tumors, i.e. the bounding boxes of renal tumors. The framework includes pseudo masks generation, group and weighted training phases. Clinical abdominal CT angiographic images of 200 patients were applied to perform the evaluation. Results: Extensive experimental results show that the proposed method achieves a higher dice coefficient (DSC) of 0.826 than the other two existing weakly-supervised deep neural networks. Furthermore, the segmentation performance is close to the fully supervised deep CNN. Conclusions: The proposed strategy improves not only the efficiency of network training but also the precision of the segmentation.