اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPDO-e$text{S}^text{2}$CNNs: Partial Differential Operator Based Equivariant Spherical CNNs
90
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Spherical signals exist in many applications, e.g., planetary data, LiDAR scans and digitalization of 3D objects, calling for models that can process spherical data effectively. It does not perform well when simply projecting spherical data into the 2D plane and then using planar convolution neural networks (CNNs), because of the distortion from projection and ineffective translation equivariance. Actually, good principles of designing spherical CNNs are avoiding distortions and converting the shift equivariance property in planar CNNs to rotation equivariance in the spherical domain. In this work, we use partial differential operators (PDOs) to design a spherical equivariant CNN, PDO-e$text{S}^text{2}$CNN, which is exactly rotation equivariant in the continuous domain. We then discretize PDO-e$text{S}^text{2}$CNNs, and analyze the equivariance error resulted from discretization. This is the first time that the equivariance error is theoretically analyzed in the spherical domain. In experiments, PDO-e$text{S}^text{2}$CNNs show greater parameter efficiency and outperform other spherical CNNs significantly on several tasks.
قيم البحث
اقرأ أيضاً
We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverage
s these symmetries in a principled manner. We present a visual analysis showing improved stability on predictions, and demonstrate that exploiting rotation equivariance significantly improves tumor detection performance on a challenging lymph node metastases dataset. We further present a novel derived dataset to enable principled comparison of machine learning models, in combination with an initial benchmark. Through this dataset, the task of histopathology diagnosis becomes accessible as a challenging benchmark for fundamental machine learning research.
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical CNN frame
work that encompasses various existing approaches and allows them to be leveraged alongside each other. The only existing non-linear spherical CNN layer that is strictly equivariant has complexity $mathcal{O}(C^2L^5)$, where $C$ is a measure of representational capacity and $L$ the spherical harmonic bandlimit. Such a high computational cost often prohibits the use of strictly equivariant spherical CNNs. We develop two new strictly equivariant layers with reduced complexity $mathcal{O}(CL^4)$ and $mathcal{O}(CL^3 log L)$, making larger, more expressive models computationally feasible. Moreover, we adopt efficient sampling theory to achieve further computational savings. We show that these developments allow the construction of more expressive hybrid models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmark problems.
Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are nevertheles
s highly computationally demanding; typically they cannot scale beyond spherical signals of thousands of pixels. We develop scattering networks constructed natively on the sphere that provide a powerful representational space for spherical data. Spherical scattering networks are computationally scalable and exhibit rotational equivariance, while their representational space is invariant to isometries and provides efficient and stable signal representations. By integrating scattering networks as an additional type of layer in the generalized spherical CNN framework, we show how they can be leveraged to scale spherical CNNs to the high-resolution data typical of many practical applications, with spherical signals of many tens of megapixels and beyond.
Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or spherical
projections, as the sphere is an unstructured grid. In this paper, we present Spherical Transformer which can transform spherical signals into vectors that can be directly processed by standard CNNs such that many well-designed CNNs architectures can be reused across tasks and datasets by pretraining. To this end, the proposed method first uses locally structured sampling methods such as HEALPix to construct a transformer grid by using the information of spherical points and its adjacent points, and then transforms the spherical signals to the vectors through the grid. By building the Spherical Transformer module, we can use multiple CNN architectures directly. We evaluate our approach on the tasks of spherical MNIST recognition, 3D object classification and omnidirectional image semantic segmentation. For 3D object classification, we further propose a rendering-based projection method to improve the performance and a rotational-equivariant model to improve the anti-rotation ability. Experimental results on three tasks show that our approach achieves superior performance over state-of-the-art methods.
Convolutional Neural Networks (CNNs) traditionally encode translation equivariance via the convolution operation. Generalization to other transformations has recently received attraction to encode the knowledge of the data geometry in group convoluti
on operations. Equivariance to rotation is particularly important for 3D image analysis due to the large diversity of possible pattern orientations. 3D texture is a particularly important cue for the analysis of medical images such as CT and MRI scans as it describes different types of tissues and lesions. In this paper, we evaluate the use of 3D group equivariant CNNs accounting for the simplified group of right-angle rotations to classify 3D synthetic textures from a publicly available dataset. The results validate the importance of rotation equivariance in a controlled setup and yet motivate the use of a finer coverage of orientations in order to obtain equivariance to realistic rotations present in 3D textures.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
