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In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric learning. Like softmax-based formulation for metric learning, it models $p(y=c|x')$, which is a probability that a query point $x'$ belongs to a class $c$. The DR formulation has two useful properties. First, the corresponding loss is not affected by scale changes of an embedding. Second, it outputs the optimal (maximum or minimum) classification confidence scores on representing points for classes. To demonstrate the effectiveness of our formulation, we conduct few-shot classification experiments using softmax-based and DR formulations on CUB and mini-ImageNet datasets. The results show that DR formulation generally enables faster and more stable metric learning than the softmax-based formulation. As a result, using DR formulation achieves improved or comparable generalization performances.

A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric Programming (GP) is combined with the ability of Sequential Quadratic Program (SQP) to accommodate a wide range of objective and constraint functions, resulting in a practical algorithm that can be adopted with little to no modification of existing design practices. Three test problems are considered to demonstrate the SLCP algorithm, comparing it with SQP and the modified Logspace Sequential Quadratic Programming (LSQP). In these cases, SLCP shows up to a 77% reduction in number of iterations compared to SQP, and an 11% reduction compared to LSQP. The airfoil analysis code XFOIL is integrated into one of the case studies to show how SLCP can be used to evolve the fidelity of design problems that have initially been modeled as GP compatible. Finally, a methodology for design based on GP and SLCP is briefly discussed.

Video Object Segmentation (VOS) is typically formulated in a semi-supervised setting. Given the ground-truth segmentation mask on the first frame, the task of VOS is to track and segment the single or multiple objects of interests in the rest frames of the video at the pixel level. One of the fundamental challenges in VOS is how to make the most use of the temporal information to boost the performance. We present an end-to-end network which stores short- and long-term video sequence information preceding the current frame as the temporal memories to address the temporal modeling in VOS. Our network consists of two temporal sub-networks including a short-term memory sub-network and a long-term memory sub-network. The short-term memory sub-network models the fine-grained spatial-temporal interactions between local regions across neighboring frames in video via a graph-based learning framework, which can well preserve the visual consistency of local regions over time. The long-term memory sub-network models the long-range evolution of object via a Simplified-Gated Recurrent Unit (S-GRU), making the segmentation be robust against occlusions and drift errors. In our experiments, we show that our proposed method achieves a favorable and competitive performance on three frequently-used VOS datasets, including DAVIS 2016, DAVIS 2017 and Youtube-VOS in terms of both speed and accuracy.

Medical image segmentation is a primary task in many applications, and the accuracy of the segmentation is a necessity. Recently, many deep learning networks derived from U-Net have been extensively used and have achieved notable results. To further improve and refine the performance of U-Net, parallel decoders along with mask prediction decoder have been carried out and have shown significant improvement with additional advantages. In our work, we utilize the advantages of using a combination of contour and distance map as regularizers. In turn, we propose a novel architecture Psi-Net with a single encoder and three parallel decoders, one decoder to learn the mask and other two to learn the auxiliary tasks of contour detection and distance map estimation. The learning of these auxiliary tasks helps in capturing the shape and boundary. We also propose a new joint loss function for the proposed architecture. The loss function consists of a weighted combination of Negative likelihood and Mean Square Error loss. We have used two publicly available datasets: 1) Origa dataset for the task of optic cup and disc segmentation and 2) Endovis segment dataset for the task of polyp segmentation to evaluate our model. We have conducted extensive experiments using our network to show our model gives better results in terms of segmentation, boundary and shape metrics.

In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of the data fitting in this formulation allows for reasonable assumptions to be made about the solution that can improve the computational performance further. In particular, we employ a well known dual formulation of this problem and solve the corresponding equations in a restricted domain. We present experimental results that explore the dependence of the solution on this restriction and quantify imrovements in the computational performance. This approach can be extended to analogous methods simply and could provide an efficient alternative for problems of this type.

Data augmentation has been widely used for training deep learning systems for medical image segmentation and plays an important role in obtaining robust and transformation-invariant predictions. However, it has seldom been used at test time for segmentation and not been formulated in a consistent mathematical framework. In this paper, we first propose a theoretical formulation of test-time augmentation for deep learning in image recognition, where the prediction is obtained through estimating its expectation by Monte Carlo simulation with prior distributions of parameters in an image acquisition model that involves image transformations and noise. We then propose a novel uncertainty estimation method based on the formulated test-time augmentation. Experiments with segmentation of fetal brains and brain tumors from 2D and 3D Magnetic Resonance Images (MRI) showed that 1) our test-time augmentation outperforms a single-prediction baseline and dropout-based multiple predictions, and 2) it provides a better uncertainty estimation than calculating the model-based uncertainty alone and helps to reduce overconfident incorrect predictions.

The per-pixel cross-entropy loss (CEL) has been widely used in structured output prediction tasks as a spatial extension of generic image classification. However, its i.i.d. assumption neglects the structural regularity present in natural images. Various attempts have been made to incorporate structural reasoning mostly through structure priors in a cooperative way where co-occuring patterns are encouraged. We, on the other hand, approach this problem from an opposing angle and propose a new framework for training such structured prediction networks via an adversarial process, in which we train a structure analyzer that provides the supervisory signals, the adversarial structure matching loss (ASML). The structure analyzer is trained to maximize ASML, or to exaggerate recurring structural mistakes usually among co-occurring patterns. On the contrary, the structured output prediction network is trained to reduce those mistakes and is thus enabled to distinguish fine-grained structures. As a result, training structured output prediction networks using ASML reduces contextual confusion among objects and improves boundary localization. We demonstrate that ASML outperforms its counterpart CEL especially in context and boundary aspects on figure-ground segmentation and semantic segmentation tasks with various base architectures, such as FCN, U-Net, DeepLab, and PSPNet.

Weak supervision, e.g., in the form of partial labels or image tags, is currently attracting significant attention in CNN segmentation as it can mitigate the lack of full and laborious pixel/voxel annotations. Enforcing high-order (global) inequality constraints on the network output, for instance, on the size of the target region, can leverage unlabeled data, guiding training with domain-specific knowledge. Inequality constraints are very flexible because they do not assume exact prior knowledge. However,constrained Lagrangian dual optimization has been largely avoided in deep networks, mainly for computational tractability reasons.To the best of our knowledge, the method of Pathak et al. is the only prior work that addresses deep CNNs with linear constraints in weakly supervised segmentation. It uses the constraints to synthesize fully-labeled training masks (proposals)from weak labels, mimicking full supervision and facilitating dual optimization.We propose to introduce a differentiable term, which enforces inequality constraints directly in the loss function, avoiding expensive Lagrangian dual iterates and proposal generation. From constrained-optimization perspective, our simple approach is not optimal as there is no guarantee that the constraints are satisfied. However, surprisingly,it yields substantially better results than the proposal-based constrained CNNs, while reducing the computational demand for training.In the context of cardiac images, we reached a segmentation performance close to full supervision using a fraction (0.1%) of the full ground-truth labels and image-level tags.While our experiments focused on basic linear constraints such as the target-region size and image tags, our framework can be easily extended to other non-linear constraints.Therefore, it has the potential to close the gap between weakly and fully supervised learning in semantic image segmentation.

This work presents a region-growing image segmentation approach based on superpixel decomposition. From an initial contour-constrained over-segmentation of the input image, the image segmentation is achieved by iteratively merging similar superpixels into regions. This approach raises two key issues: (1) how to compute the similarity between superpixels in order to perform accurate merging and (2) in which order those superpixels must be merged together. In this perspective, we firstly introduce a robust adaptive multi-scale superpixel similarity in which region comparisons are made both at content and common border level. Secondly, we propose a global merging strategy to efficiently guide the region merging process. Such strategy uses an adpative merging criterion to ensure that best region aggregations are given highest priorities. This allows to reach a final segmentation into consistent regions with strong boundary adherence. We perform experiments on the BSDS500 image dataset to highlight to which extent our method compares favorably against other well-known image segmentation algorithms. The obtained results demonstrate the promising potential of the proposed approach.

Instance segmentation is the problem of detecting and delineating each distinct object of interest appearing in an image. Current instance segmentation approaches consist of ensembles of modules that are trained independently of each other, thus missing opportunities for joint learning. Here we propose a new instance segmentation paradigm consisting in an end-to-end method that learns how to segment instances sequentially. The model is based on a recurrent neural network that sequentially finds objects and their segmentations one at a time. This net is provided with a spatial memory that keeps track of what pixels have been explained and allows occlusion handling. In order to train the model we designed a principled loss function that accurately represents the properties of the instance segmentation problem. In the experiments carried out, we found that our method outperforms recent approaches on multiple person segmentation, and all state of the art approaches on the Plant Phenotyping dataset for leaf counting.