Surface-Based Computation of the Euler Characteristic in the BCC Grid

As opposed to the 3D cubic grid, the body-centered cubic (BCC) grid has some favorable topological properties: each set of voxels in the grid is a 3-manifold, with 2-manifold boundary. Thus, the Euler characteristic of an object O in this grid can be computed as half of the Euler characteristic of its boundary ∂O . We propose three new algorithms to compute the Euler characteristic in the BCC grid with this surface-based approach: one based on (critical point) Morse theory and two based on the discrete Gauss–Bonnet theorem. We provide a comparison between the three new algorithms and the classic approach based on counting the number of cells, either of the 3D object or of its 2D boundary surface

Edge-promoting reconstruction of absorption and diffusivity in optical tomography

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged object is composed of an approximately homogeneous background with clearly distinguishable embedded inhomogeneities. An algorithm for finding the maximum a posteriori estimate for the absorption and diffusion coefficients is introduced assuming an edge-preferring prior and an additive Gaussian measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via three-dimensional numerical experiments with simulated measurement data.Comment: 18 pages, 6 figure

Non-Euclidean classification of medically imaged objects via s-reps

AbstractClassifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes full advantage of the geometry of the manifold on which these non-Euclidean geometric object properties (GOPs) live. Our method is evaluated via the task of classifying 3D hippocampi between schizophrenics and healthy controls. We address three central questions. 1) Does adding shape features increase discriminative power over the more standard classification based only on global volume? 2) If so, does our skeletal representation provide greater discriminative power than a conventional boundary point distribution model (PDM)? 3) Especially, is Euclideanization of non-Euclidean shape properties important in achieving high discriminative power? Measuring the capability of a method in terms of area under the receiver operator characteristic (ROC) curve, we show that our proposed method achieves strongly better classification than both the classification method based on global volume alone and the s-rep-based classification method without proper Euclideanization of non-Euclidean GOPs. We show classification using Euclideanized s-reps is also superior to classification using PDMs, whether the PDMs are first Euclideanized or not. We also show improved performance with Euclideanized boundary PDMs over non-linear boundary PDMs. This demonstrates the benefit that proper Euclideanization of non-Euclidean GOPs brings not only to s-rep-based classification but also to PDM-based classification

A Comparative Analysis of the Zernike Moments for Single Object Retrieval

تم استخدام لحظات زينرك بشكل شائع في العديد من دراسات استرجاع الصور المبنية على الأشكال بسبب تمثيلها القوي للأشكال.ومع ذلك لم يتم تسليط الضوء بوضوح على نقاط قوتها وضعفها في الدراسات السابقة. وبالتالي، لا يمكن استغلال تمثيلها القوي بشكل كامل.في هذه االدراسة، يتم تنفيذ طريقة لالتقاط خصائص تمثيل الأشكال في لحظات زينرك بالكامل وتطبيقها على كائن واحد للحصول على صورثنائية ومستوى رمادي. تعمل الطريقة المقترحة عن طريق تحديد حدود كائن الشكل ثم تغيير حجم شكل الكائن إلى حدود الصورة. تم إجراءثلاث دراسات حالة. الحالة 1 هي تطبيق لحظات زينرك على صورة كائن الشكل الأصلي. في الحالة 2 ، يتم نقل النقطة الوسطى لصورةكائن الشكل في الحالة 1 إلى مركز الصورة. في الحالة 3 ، تقوم الطريقة المقترحة أولاً باكتشاف الحدود الخارجية لشكل الكائن ثم تغيير حجمالكائن إلى حد الصورة. تم إجراء تحقيقات تجريبية باستخدام مجموعتي بيانات صورتين قياسيتين أظهرت أن الطريقة المقترحة في الحالة 3قد تم توضيحها لتوفير أفضل أداء لاسترجاع الصور مقارنةً بكل من 1 و 2 . الخلاصة تتلخص ان لالتقاط الصورة بشكل كامل خصائص تمثيلالشكل القوية للحظة زينرك ، يجب تغيير حجم كائن الشكل إلى حدود الصورة .Zernike Moments has been popularly used in many shape-based image retrieval studies due to its powerful shape representation. However its strength and weaknesses have not been clearly highlighted in the previous studies. Thus, its powerful shape representation could not be fully utilized. In this paper, a method to fully capture the shape representation properties of Zernike Moments is implemented and tested on a single object for binary and grey level images. The proposed method works by determining the boundary of the shape object and then resizing the object shape to the boundary of the image. Three case studies were made. Case 1 is the Zernike Moments implementation on the original shape object image. In Case 2, the centroid of the shape object image in Case 1 is relocated to the center of the image. In Case 3, the proposed method first detect the outer boundary of the shape object and then resizing the object to the boundary of the image. Experimental investigations were made by using two benchmark shape image datasets showed that the proposed method in Case 3 had demonstrated to provide the most superior image retrieval performances as compared to both the Case 1 and Case 2. As a conlusion, to fully capture the powerful shape representation properties of the Zernike moment, a shape object should be resized to the boundary of the image

Enhanced Boundary Learning for Glass-like Object Segmentation

Glass-like objects such as windows, bottles, and mirrors exist widely in the real world. Sensing these objects has many applications, including robot navigation and grasping. However, this task is very challenging due to the arbitrary scenes behind glass-like objects. This paper aims to solve the glass-like object segmentation problem via enhanced boundary learning. In particular, we first propose a novel refined differential module that outputs finer boundary cues. We then introduce an edge-aware point-based graph convolution network module to model the global shape along the boundary. We use these two modules to design a decoder that generates accurate and clean segmentation results, especially on the object contours. Both modules are lightweight and effective: they can be embedded into various segmentation models. In extensive experiments on three recent glass-like object segmentation datasets, including Trans10k, MSD, and GDD, our approach establishes new state-of-the-art results. We also illustrate the strong generalization properties of our method on three generic segmentation datasets, including Cityscapes, BDD, and COCO Stuff. Code and models is available at \url{https://github.com/hehao13/EBLNet}.Comment: ICCV-2021 Code is availabe at https://github.com/hehao13/EBLNe