Foveation for Segmentation of Mega-Pixel Histology Images

Segmenting histology images is challenging because of the sheer size of the images with millions or even billions of pixels. Typical solutions pre-process each histology image by dividing it into patches of fixed size and/or down-sampling to meet memory constraints. Such operations incur information loss in the field-of-view (FoV) (i.e., spatial coverage) and the image resolution. The impact on segmentation performance is, however, as yet understudied. In this work, we first show under typical memory constraints (e.g., 10G GPU memory) that the trade-off between FoV and resolution considerably affects segmentation performance on histology images, and its influence also varies spatially according to local patterns in different areas (see Fig. 1). Based on this insight, we then introduce foveation module, a learnable “dataloader” which, for a given histology image, adaptively chooses the appropriate configuration (FoV/resolution trade-off) of the input patch to feed to the downstream segmentation model at each spatial location (Fig. 1). The foveation module is jointly trained with the segmentation network to maximise the task performance. We demonstrate, on the Gleason2019 challenge dataset for histopathology segmentation, that the foveation module improves segmentation performance over the cases trained with patches of fixed FoV/resolution trade-off. Moreover, our model achieves better segmentation accuracy for the two most clinically important and ambiguous classes (Gleason Grade 3 and 4) than the top performers in the challenge by 13.1% and 7.5%, and improves on the average performance of 6 human experts by 6.5% and 7.5%

LEARNING TO DOWNSAMPLE FOR SEGMENTATION OF ULTRA-HIGH RESOLUTION IMAGES

Many computer vision systems require low-cost segmentation algorithms based on deep learning, either because of the enormous size of input images or limited computational budget. Common solutions uniformly downsample the input images to meet memory constraints, assuming all pixels are equally informative. In this work, we demonstrate that this assumption can harm the segmentation performance because the segmentation difficulty varies spatially (see Figure 1 “Uniform”). We combat this problem by introducing a learnable downsampling module, which can be optimised together with the given segmentation model in an end-to-end fashion. We formulate the problem of training such downsampling module as optimisation of sampling density distributions over the input images given their low-resolution views. To defend against degenerate solutions (e.g. over-sampling trivial regions like the backgrounds), we propose a regularisation term that encourages the sampling locations to concentrate around the object boundaries. We find the downsampling module learns to sample more densely at difficult locations, thereby improving the segmentation performance (see Figure 1 "Ours"). Our experiments on benchmarks of high-resolution street view, aerial and medical images demonstrate substantial improvements in terms of efficiency-and-accuracy trade-off compared to both uniform downsampling and two recent advanced downsampling techniques

Bi-Legendrian manifolds and paracontact geometry

We study the interplays between paracontact geometry and the theory of bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a bi-Legendrian manifold M as the paracontact connection of a canonical paracontact structure induced on M and then we discuss many consequences of this result both for bi-Legendrian and for paracontact manifolds. Finally new classes of examples of paracontact manifolds are presented.Comment: to appear in Int. J. Geom. Meth. Mod. Phy

Energy properness and Sasakian-Einstein metrics

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page

Penrose type inequalities for asymptotically hyperbolic graphs

In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space \bH^n. The graphs are considered as subsets of \bH^{n+1} and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.Comment: 29 pages, no figure, includes a proof of the equality cas

3-quasi-Sasakian manifolds

In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update

(Re)constructing Dimensions

Compactifying a higher-dimensional theory defined in R^{1,3+n} on an n-dimensional manifold {\cal M} results in a spectrum of four-dimensional (bosonic) fields with masses m^2_i = \lambda_i, where - \lambda_i are the eigenvalues of the Laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and K\"{a}hler and so they are isospectral backgrounds for string theory. Utilizing results from finite spectral geometry, we also discuss the accuracy of reconstructing the properties of the compact manifold (e.g., its dimension, volume, and curvature etc) from measuring the masses of only a finite number of Kaluza-Klein modes.Comment: 23 pages, 3 figures, 2 references adde

Early experience with targeted therapy and dendritic cell vaccine in metastatic renal cell carcinoma after nephrectomy

PURPOSE: Metastatic renal cell carcinoma (RCC) is one of the most treatment-resistant malignancies and nephrectomy, isolated or combined with systemic chemotherapy typically has limited or no effectiveness. We report our initial results in patients treated with the association of molecular targeted therapy, nephrectomy, and hybrid dendritic-tumor cell (DC) vaccine. MATERIALS AND METHODS: Two male patients diagnosed with metastatic RCC were selected for the study. They were treated with the triple strategy, in which sunitinib (50 mg per day) was given for 4 weeks, followed by radical nephrectomy after two weeks. DC vaccine was initiated immediately after surgery and repeated monthly. Sunitinib was restarted daily after 2 to 3 weeks of surgery with a 7-day interval every 4 weeks. RESULTS: Both patients had complete adherence to the proposed treatment with DC vaccine therapy combined with sunitinib. Follow-up in these patients at 9 and 10 months demonstrated a stable disease in both, as shown by imaging and clinical findings, with no further treatment required. CONCLUSION: The immune response obtained with DC vaccine combined with the antiangiogenic effect of sunitinib and the potential benefits of cytoreductive nephrectomy in advanced disease could represent a new option in the treatment of metastatic RCC. Further prospective trials are needed not only to elucidate the ideal dosing and schedule, but also to better define the proof-of-concept proposed in this report and its role in clinical practice

Let's Agree to Disagree: Learning Highly Debatable Multirater Labelling

Classification and differentiation of small pathological objects may greatly vary among human raters due to differences in training, expertise and their consistency over time. In a radiological setting, objects commonly have high within-class appearance variability whilst sharing certain characteristics across different classes, making their distinction even more difficult. As an example, markers of cerebral small vessel disease, such as enlarged perivascular spaces (EPVS) and lacunes, can be very varied in their appearance while exhibiting high inter-class similarity, making this task highly challenging for human raters. In this work, we investigate joint models of individual rater behaviour and multi-rater consensus in a deep learning setting, and apply it to a brain lesion object-detection task. Results show that jointly modelling both individual and consensus estimates leads to significant improvements in performance when compared to directly predicting consensus labels, while also allowing the characterization of human-rater consistency