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Register a new userBandwidth selection for kernel estimation in mixed multi-dimensional spaces
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Added by
Aurelie Bugeau
Publication date
2007
fields
Informatics Engineering
and research's language is
English
Authors
Aurelie Bugeau
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Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real challenge in case of multidimensional heterogeneous features. This paper presents a solution to this problem. It is an extension of cite{Comaniciu03a} which was based on the fundamental property of normal distributions regarding the bias of the normalized density gradient. The selection is done iteratively for each type of features, by looking for the stability of local bandwidth estimates across a predefined range of bandwidths. A pseudo balloon mean shift filtering and partitioning are introduced. The validity of the method is demonstrated in the context of color image segmentation based on a 5-dimensional space.
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Existing video-based human pose estimation methods extensively apply large networks onto every frame in the video to localize body joints, which suffer high computational cost and hardly meet the low-latency requirement in realistic applications. To address this issue, we propose a novel Dynamic Kernel Distillation (DKD) model to facilitate small networks for estimating human poses in videos, thus significantly lifting the efficiency. In particular, DKD introduces a light-weight distillator to online distill pose kernels via leveraging temporal cues from the previous frame in a one-shot feed-forward manner. Then, DKD simplifies body joint localization into a matching procedure between the pose kernels and the current frame, which can be efficiently computed via simple convolution. In this way, DKD fast transfers pose knowledge from one frame to provide compact guidance for body joint localization in the following frame, which enables utilization of small networks in video-based pose estimation. To facilitate the training process, DKD exploits a temporally adversarial training strategy that introduces a temporal discriminator to help generate temporally coherent pose kernels and pose estimation results within a long range. Experiments on Penn Action and Sub-JHMDB benchmarks demonstrate outperforming efficiency of DKD, specifically, 10x flops reduction and 2x speedup over previous best model, and its state-of-the-art accuracy.
Recent contributions to kernel smoothing show that the performance of cross-validated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classical cross-validated bandwidth from a more rough and difficult smoothing problem than the original one and then rescales this indirect bandwidth to become a bandwidth of the original problem. The motivation for this approach comes from the observation that classical crossvalidation tends to work better when the smoothing problem is difficult. In this paper we find that the performance of indirect crossvalidation improves theoretically and practically when the polynomial order of the indirect kernel increases, with the Gaussian kernel as limiting kernel when the polynomial order goes to infinity. These theoretical and practical results support the often proposed choice of the Gaussian kernel as indirect kernel. However, for do-validation our study shows a discrepancy between asymptotic theory and practical performance. As for indirect crossvalidation, in asymptotic theory the performance of indirect do-validation improves with increasing polynomial order of the used indirect kernel. But this theoretical improvements do not carry over to practice and the original do-validation still seems to be our preferred bandwidth selector. We also consider plug-in estimation and combinations of plug-in bandwidths and crossvalidated bandwidths. These latter bandwidths do not outperform the original do-validation estimator either.
We present a method for image-based crowd counting, one that can predict a crowd density map together with the uncertainty values pertaining to the predicted density map. To obtain prediction uncertainty, we model the crowd density values using Gaussian distributions and develop a convolutional neural network architecture to predict these distributions. A key advantage of our method over existing crowd counting methods is its ability to quantify the uncertainty of its predictions. We illustrate the benefits of knowing the prediction uncertainty by developing a method to reduce the human annotation effort needed to adapt counting networks to a new domain. We present sample selection strategies which make use of the density and uncertainty of predictions from the networks trained on one domain to select the informative images from a target domain of interest to acquire human annotation. We show that our sample selection strategy drastically reduces the amount of labeled data from the target domain needed to adapt a counting network trained on a source domain to the target domain. Empirically, the networks trained on UCF-QNRF dataset can be adapted to surpass the performance of the previous state-of-the-art results on NWPU dataset and Shanghaitech dataset using only 17$%$ of the labeled training samples from the target domain.
High-dimensional variable selection is an important issue in many scientific fields, such as genomics. In this paper, we develop a sure independence feature screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS, for short). KCCA- SIS is easy to be implemented and applied. Compared to the sure independence screen- ing procedure based on the Pearson correlation (SIS, for short) developed by Fan and Lv [2008], KCCA-SIS can handle nonlinear dependencies among variables. Compared to the sure independence screening procedure based on the distance correlation (DC- SIS, for short) proposed by Li et al. [2012], KCCA-SIS is scale free, distribution free and has better approximation results based on the universal characteristic of Gaussian Kernel (Micchelli et al. [2006]). KCCA-SIS is more general than SIS and DC-SIS in the sense that SIS and DC-SIS correspond to certain choice of kernels. Compared to supremum of Hilbert Schmidt independence criterion-Sure independence screening (sup-HSIC-SIS, for short) developed by Balasubramanian et al. [2013], KCCA-SIS is scale free removing the marginal variation of features and response variables. No model assumption is needed between response and predictors to apply KCCA-SIS and it can be used in ultrahigh dimensional data analysis. Similar to DC-SIS and sup- HSIC-SIS, KCCA-SIS can also be used directly to screen grouped predictors and for multivariate response variables. We show that KCCA-SIS has the sure screening prop- erty, and has better performance through simulation studies. We applied KCCA-SIS to study Autism genes in a spatiotemporal gene expression dataset for human brain development, and obtained better results based on gene ontology enrichment analysis comparing to the other existing methods.
Existing blind image super-resolution (SR) methods mostly assume blur kernels are spatially invariant across the whole image. However, such an assumption is rarely applicable for real images whose blur kernels are usually spatially variant due to factors such as object motion and out-of-focus. Hence, existing blind SR methods would inevitably give rise to poor performance in real applications. To address this issue, this paper proposes a mutual affine network (MANet) for spatially variant kernel estimation. Specifically, MANet has two distinctive features. First, it has a moderate receptive field so as to keep the locality of degradation. Second, it involves a new mutual affine convolution (MAConv) layer that enhances feature expressiveness without increasing receptive field, model size and computation burden. This is made possible through exploiting channel interdependence, which applies each channel split with an affine transformation module whose input are the rest channel splits. Extensive experiments on synthetic and real images show that the proposed MANet not only performs favorably for both spatially variant and invariant kernel estimation, but also leads to state-of-the-art blind SR performance when combined with non-blind SR methods.
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