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Non-small-cell lung cancer (NSCLC) represents approximately 80–85% of lung cancer diagnoses and is the leading cause of cancer-related death worldwide. Recent studies indicate that image-based radiomics features from positron emission tomography/computed tomography (PET/CT) images have predictive power for NSCLC outcomes. To this end, easily calculated functional features such as the maximum and the mean of standard uptake value (SUV) and total lesion glycolysis (TLG) are most commonly used for NSCLC prognostication, but their prognostic value remains controversial. Meanwhile, convolutional neural networks (CNN) are rapidly emerging as a new method for cancer image analysis, with significantly enhanced predictive power compared to hand-crafted radiomics features. Here we show that CNNs trained to perform the tumor segmentation task, with no other information than physician contours, identify a rich set of survival-related image features with remarkable prognostic value. In a retrospective study on pre-treatment PET-CT images of 96 NSCLC patients before stereotactic-body radiotherapy (SBRT), we found that the CNN segmentation algorithm (U-Net) trained for tumor segmentation in PET and CT images, contained features having strong correlation with 2- and 5-year overall and disease-specific survivals. The U-Net algorithm has not seen any other clinical information (e.g. survival, age, smoking history, etc.) than the images and the corresponding tumor contours provided by physicians. In addition, we observed the same trend by validating the U-Net features against an extramural data set provided by Stanford Cancer Institute. Furthermore, through visualization of the U-Net, we also found convincing evidence that the regions of metastasis and recurrence appear to match with the regions where the U-Net features identified patterns that predicted higher likelihoods of death. We anticipate our findings will be a starting point for more sophisticated non-intrusive patient specific cancer prognosis determination. For example, the deep learned PET/CT features can not only predict survival but also visualize high-risk regions within or adjacent to the primary tumor and hence potentially impact therapeutic outcomes by optimal selection of therapeutic strategy or first-line therapy adjustment.

A robust and informative local shape descriptor plays an important role in mesh registration. In this regard, spectral descriptors that are based on the spectrum of the Laplace-Beltrami operator have gained a spotlight among the researchers for the last decade due to their desirable properties, such as isometry invariance. Despite such, however, spectral descriptors often fail to give a correct similarity measure for non-isometric cases where the metric distortion between the models is large. Hence, they are in general not suitable for the registration problems, except for the special cases when the models are near-isometry. In this paper, we investigate a way to develop shape descriptors for non-isometric registration tasks by embedding the spectral shape descriptors into a different metric space where the Euclidean distance between the elements directly indicates the geometric dissimilarity. We design and train a Siamese deep neural network to find such an embedding, where the embedded descriptors are promoted to rearrange based on the geometric similarity. We found our approach can significantly enhance the performance of the conventional spectral descriptors for the non-isometric registration tasks, and outperforms recent state-of-the-art methods reported in literature.

In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two‐dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid‐like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid‐like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.

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