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Register a new user3D Solid Spherical Bispectrum CNNs for Biomedical Texture Analysis
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Added by
Valentin Oreiller
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Locally Rotation Invariant (LRI) operators have shown great potential in biomedical texture analysis where patterns appear at random positions and orientations. LRI operators can be obtained by computing the responses to the discrete rotation of local descriptors, such as Local Binary Patterns (LBP) or the Scale Invariant Feature Transform (SIFT). Other strategies achieve this invariance using Laplacian of Gaussian or steerable wavelets for instance, preventing the introduction of sampling errors during the discretization of the rotations. In this work, we obtain LRI operators via the local projection of the image on the spherical harmonics basis, followed by the computation of the bispectrum, which shares and extends the invariance properties of the spectrum. We investigate the benefits of using the bispectrum over the spectrum in the design of a LRI layer embedded in a shallow Convolutional Neural Network (CNN) for 3D image analysis. The performance of each design is evaluated on two datasets and compared against a standard 3D CNN. The first dataset is made of 3D volumes composed of synthetically generated rotated patterns, while the second contains malignant and benign pulmonary nodules in Computed Tomography (CT) images. The results indicate that bispectrum CNNs allows for a significantly better characterization of 3D textures than both the spectral and standard CNN. In addition, it can efficiently learn with fewer training examples and trainable parameters when compared to a standard convolutional layer.
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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 convolution 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.
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 framework 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) 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.
Contrasting the previous evidence that neurons in the later layers of a Convolutional Neural Network (CNN) respond to complex object shapes, recent studies have shown that CNNs actually exhibit a `texture bias: given an image with both texture and shape cues (e.g., a stylized image), a CNN is biased towards predicting the category corresponding to the texture. However, these previous studies conduct experiments on the final classification output of the network, and fail to robustly evaluate the bias contained (i) in the latent representations, and (ii) on a per-pixel level. In this paper, we design a series of experiments that overcome these issues. We do this with the goal of better understanding what type of shape information contained in the network is discriminative, where shape information is encoded, as well as when the network learns about object shape during training. We show that a network learns the majority of overall shape information at the first few epochs of training and that this information is largely encoded in the last few layers of a CNN. Finally, we show that the encoding of shape does not imply the encoding of localized per-pixel semantic information. The experimental results and findings provide a more accurate understanding of the behaviour of current CNNs, thus helping to inform future design choices.
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.
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