Abstract This paper introduces SensoGraph, a novel approach for fast sensory evaluation using two-dimensional geometric techniques. In the tasting sessions, the assessors follow their own criteria to place samples on a tablecloth, according to the similarity between samples. In order to analyse the data collected, first a geometric clustering is performed to each tablecloth, extracting connections between the samples. Then, these connections are used to construct a global similarity matrix. Finally, a graph drawing algorithm is used to obtain a 2D consensus graphic, which reflects the global opinion of the panel by (1) positioning closer those samples that have been globally perceived as similar and (2) showing the strength of the connections between samples. The proposal is validated by performing four tasting sessions, with three types of panels tasting different wines, and by developing a new software to implement the proposed techniques. The results obtained show that the graphics provide similar positionings of the samples as the consensus maps obtained by multiple factor analysis (MFA), further providing extra information about connections between samples, not present in any previous method. The main conclusion is that the use of geometric techniques provides information complementary to MFA, and of a different type. Finally, the method proposed is computationally able to manage a significantly larger number of assessors than MFA, which can be useful for the comparison of pictures by a huge number of consumers, via the Internet.
Thus, several alternative methods have arisen in the last years , aiming to provide a fast sensory positioning of a set of products by assessors who are not necessarily trained. Skipping the need to train the panellists allows to elude the need of waiting a long time before obtaining results, as well as the need of agreeing on particular attributes, which may become difficult when working with experts like wine professionals or chefs . Introduced by @cite_2 @cite_10 , Projective Mapping asks the assessors to position the presented samples on a two-dimensional space, usually a blank sheet of paper as tablecloth, following their own criteria: The more similar they perceive two samples, the closer they should position them, and vice versa . In those seminal works, the data were analysed by generalized procrustes analysis (GPA) and principal component analysis (PCA) , using the RV coefficient to compare the method with conventional profiling.
@cite_10 @cite_2
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Abstract This paper deals with the method of projective mapping and its use in sensory analysis. Projective mapping is a method which allows naive consumers to map products on a two dimension space, based on similarities and differences in the products. An experiment was carried out on seven blueberry soups, whereby sensory profiling was undertaken using a trained panel and projective mapping. Preference assessment was undertaken using a small group of consumers. Results indicated that the three replicates of the mapping exercise produced visually very similar maps, at least on the first two dimensions. However, it was found that consumers perceived the samples in somewhat different ways as high-lighted by RV coefficients. The consensus mapping dimensions were compared to those from the profile data, and it was apparent that the best similarity was found when comparing the first dimension, thus suggesting good agreement on the obvious aspects of the product. The internal preference map also revealed major product contrasts along this dimension with some weak evidence of segmentation. The overall conclusion of this paper raises further fundamental questions about consensus spaces with consumers, and the question of dimensionality of consumer perception as compared to trained panels. Abstract Studies have indicated that profiling and (dis)similarity scaling yield different perceptual product maps. Conceptually, these two procedures are different. This paper looks at a third and alternative method of producing a two-dimensional, perceptual map utilizing a projective-type method whereby individual assessors themselves are required to place products on the space according to the similarities and differences they perceive. However, visual comparison of the final results provided by each assessor is difficult and, hence, generalized Procrustes analysis is applied to compare each assessor's map for similarity with the others. In this study it was found that the perceptual map derived from projective mapping was as similar to the map derived from profiling as from dissimilarity scaling. However, consistency over repeated trials was greater for projective mapping than for the other two methods. It is suggested that projective mapping could be a potentially useful technique for linking sensory analysis and consumer research data. High correlation among the neighboring pixels both spatially and spectrally in a multispectral image makes it necessary to use an efficient data transformation approach before performing pan-sharpening. Wavelets and principal component analysis (PCA) methods have been a popular choice for spatial and spectral transformations, respectively. Current PCA-based pan-sharpening methods make an assumption that the first principal component (PC) of high variance is an ideal choice for replacing or injecting it with high spatial details from the high-resolution histogram-matched panchromatic (PAN) image. This paper presents a combined adaptive PCA-contourlet approach for pan-sharpening, where the adaptive PCA is used to reduce the spectral distortion and the use of nonsubsampled contourlets for spatial transformation in pan-sharpening is incorporated to overcome the limitation of the wavelets in representing the directional information efficiently and capturing intrinsic geometrical structures of the objects. The efficiency of the presented method is tested by performing pan-sharpening of the high-resolution (IKONOS and QuickBird) and the medium-resolution (Landsat-7 Enhanced Thematic Mapper Plus) datasets. The evaluation of the pan-sharpened images using global validation indexes reveal that the adaptive PCA approach helps reducing the spectral distortion, and its merger with contourlets provides better fusion results. Statistical methods are of paramount importance in discovering the modes of variation in visual data. The Principal Component Analysis (PCA) is probably the most prominent method for extracting a single mode of variation in the data. However, in practice, several factors contribute to the appearance of visual objects including pose, illumination, and deformation, to mention a few. To extract these modes of variations from visual data, several supervised methods, such as the TensorFaces relying on multilinear (tensor) decomposition have been developed. The main drawbacks of such methods is that they require both labels regarding the modes of variations and the same number of samples under all modes of variations (e.g., the same face under different expressions, poses etc.). Therefore, their applicability is limited to well-organised data, usually captured in well-controlled conditions. In this paper, we propose a novel general multilinear matrix decomposition method that discovers the multilinear structure of possibly incomplete sets of visual data in unsupervised setting (i.e., without the presence of labels). We also propose extensions of the method with sparsity and low-rank constraints in order to handle noisy data, captured in unconstrained conditions. Besides that, a graph-regularised variant of the method is also developed in order to exploit available geometric or label information for some modes of variations. We demonstrate the applicability of the proposed method in several computer vision tasks, including Shape from Shading (SfS) (in the wild and with occlusion removal), expression transfer, and estimation of surface normals from images captured in the wild. When faced with high-dimensional data, one often uses principal component analysis (PCA) for dimension reduction. Classical PCA constructs a set of uncorrelated variables, which correspond to eigenvectors of the sample covariance matrix. However, it is well-known that this covariance matrix is strongly affected by anomalous observations. It is therefore necessary to apply robust methods that are resistant to possible outliers. Li and Chen [J. Am. Stat. Assoc. 80 (1985) 759] proposed a solution based on projection pursuit (PP). The idea is to search for the direction in which the projected observations have the largest robust scale. In subsequent steps, each new direction is constrained to be orthogonal to all previous directions. This method is very well suited for high-dimensional data, even when the number of variables p is higher than the number of observations n. However, the algorithm of Li and Chen has a high computational cost. In the references [C. Croux, A. Ruiz-Gazen, in COMPSTAT: Proceedings in Computational Statistics 1996, Physica-Verlag, Heidelberg, 1996, pp. 211–217; C. Croux and A. Ruiz-Gazen, High Breakdown Estimators for Principal Components: the Projection-Pursuit Approach Revisited, 2000, submitted for publication.], a computationally much more attractive method is presented, but in high dimensions (large p) it has a numerical accuracy problem and still consumes much computation time. In this paper, we construct a faster two-step algorithm that is more stable numerically. The new algorithm is illustrated on a data set with four dimensions and on two chemometrical data sets with 1200 and 600 dimensions. We present an algorithm for automatic image orientation estimation using a Bayesian learning framework. We demonstrate that a small codebook (the optimal size of codebook is selected using a modified MDL criterion) extracted from a learning vector quantizer (LVQ) can be used to estimate the class-conditional densities of the observed features needed for the Bayesian methodology. We further show how principal component analysis (PCA) and linear discriminant analysis (LDA) can be used as a feature extraction mechanism to remove redundancies in the high-dimensional feature vectors used for classification. The proposed method is compared with four different commonly used classifiers, namely k-nearest neighbor, support vector machine (SVM), a mixture of Gaussians, and hierarchical discriminating regression (HDR) tree. Experiments on a database of 16 344 images have shown that our proposed algorithm achieves an accuracy of approximately 98 on the training set and over 97 on an independent test set. A slight improvement in classification accuracy is achieved by employing classifier combination techniques. We present a novel algorithm to produce descriptive online 3D occupancy maps using Gaussian processes (GPs). GP regression and classification have met with recent success in their application to robot mapping, as GPs are capable of expressing rich correlation among map cells and sensor data. However, the cubic computational complexity has limited its application to large-scale mapping and online use. In this paper we address this issue first by proposing test-data octrees, octrees within blocks of the map that prune away nodes of the same state, condensing the number of test data used in a regression, in addition to allowing fast data retrieval. We also propose a nested Bayesian committee machine which, after new sensor data is partitioned among several GP regressions, fuses the result and updates the map with greatly reduced complexity. Finally, by adjusting the range of influence of the training data and tuning a variance threshold implemented in our method's binary classification step, we are able to control the richness of inference achieved by GPs - and its tradeoff with classification accuracy. The performance of the proposed approach is evaluated with both simulated and real data, demonstrating that the method may serve both as an improved-accuracy classifier, and as a predictive tool to support autonomous navigation. The seminal multiple-view stereo benchmark evaluations from Middlebury and by have played a major role in propelling the development of multi-view stereopsis (MVS) methodology. The somewhat small size and variability of these data sets, however, limit their scope and the conclusions that can be derived from them. To facilitate further development within MVS, we here present a new and varied data set consisting of 80 scenes, seen from 49 or 64 accurate camera positions. This is accompanied by accurate structured light scans for reference and evaluation. In addition all images are taken under seven different lighting conditions. As a benchmark and to validate the use of our data set for obtaining reasonable and statistically significant findings about MVS, we have applied the three state-of-the-art MVS algorithms by , , and to the data set. To do this we have extended the evaluation protocol from the Middlebury evaluation, necessitated by the more complex geometry of some of our scenes. The data set and accompanying evaluation framework are made freely available online. Based on this evaluation, we are able to observe several characteristics of state-of-the-art MVS, e.g. that there is a tradeoff between the quality of the reconstructed 3D points (accuracy) and how much of an object's surface is captured (completeness). Also, several issues that we hypothesized would challenge MVS, such as specularities and changing lighting conditions did not pose serious problems. Our study finds that the two most pressing issues for MVS are lack of texture and meshing (forming 3D points into closed triangulated surfaces). In this paper we present a generalization of classical multidimensional scaling called DISTATIS which is a new method that can be used to compare algorithms when their outputs consist of distance matrices computed on the same set of objects. The method first evaluates the similarity between algorithms using a coefficient called the RV coefficient. From this analysis, a compromise matrix is computed which represents the best aggregate of the original matrices. In order to evaluate the differences between algorithms, the original distance matrices are then projected onto the compromise. We illustrate this method with a "toy example" in which four different "algorithms" (two computer programs and two sets of human observers) evaluate the similarity among faces. Given a set of images of scenes containing multiple object categories (e.g. grass, roads, buildings) our objective is to discover these objects in each image in an unsupervised manner, and to use this object distribution to perform scene classification. We achieve this discovery using probabilistic Latent Semantic Analysis (pLSA), a generative model from the statistical text literature, here applied to a bag of visual words representation for each image. The scene classification on the object distribution is carried out by a k-nearest neighbour classifier. We investigate the classification performance under changes in the visual vocabulary and number of latent topics learnt, and develop a novel vocabulary using colour SIFT descriptors. Classification performance is compared to the supervised approaches of Vogel & Schiele [19] and Oliva & Torralba [11], and the semi-supervised approach of Fei Fei & Perona [3] using their own datasets and testing protocols. In all cases the combination of (unsupervised) pLSA followed by (supervised) nearest neighbour classification achieves superior results. We show applications of this method to image retrieval with relevance feedback and to scene classification in videos. In this paper we introduce a new underlying probabilistic model for principal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior's covariance function constrains the mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance functions which allow non-linear mappings. This more general Gaussian process latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our non-linear algorithm can be further kernelised leading to 'twin kernel PCA' in which a mapping between feature spaces occurs. Visual search and image retrieval underpin numerous applications, however the task is still challenging predominantly due to the variability of object appearance and ever increasing size of the databases, often exceeding billions of images. Prior art methods rely on aggregation of local scale-invariant descriptors, such as SIFT, via mechanisms including Bag of Visual Words (BoW), Vector of Locally Aggregated Descriptors (VLAD) and Fisher Vectors (FV). However, their performance is still short of what is required. This paper presents a novel method for deriving a compact and distinctive representation of image content called Robust Visual Descriptor with Whitening (RVD-W). It significantly advances the state of the art and delivers world-class performance. In our approach local descriptors are rank-assigned to multiple clusters. Residual vectors are then computed in each cluster, normalized using a direction-preserving normalization function and aggregated based on the neighborhood rank. Importantly, the residual vectors are de-correlated and whitened in each cluster before aggregation, leading to a balanced energy distribution in each dimension and significantly improved performance. We also propose a new post-PCA normalization approach which improves separability between the matching and non-matching global descriptors. This new normalization benefits not only our RVD-W descriptor but also improves existing approaches based on FV and VLAD aggregation. Furthermore, we show that the aggregation framework developed using hand-crafted SIFT features also performs exceptionally well with Convolutional Neural Network (CNN) based features. The RVD-W pipeline outperforms state-of-the-art global descriptors on both the Holidays and Oxford datasets. On the large scale datasets, Holidays1M and Oxford1M, SIFT-based RVD-W representation obtains a mAP of 45.1 and 35.1 percent, while CNN-based RVD-W achieve a mAP of 63.5 and 44.8 percent, all yielding superior performance to the state-of-the-art. Principal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. To facilitate interpretation, sparse PCA produces modified PCs with sparse loadings, i.e. loadings with very few non-zero elements. In this paper, we propose a new sparse PCA method, namely sparse PCA via regularized SVD (sPCA-rSVD). We use the connection of PCA with singular value decomposition (SVD) of the data matrix and extract the PCs through solving a low rank matrix approximation problem. Regularization penalties are introduced to the corresponding minimization problem to promote sparsity in PC loadings. An efficient iterative algorithm is proposed for computation. Two tuning parameter selection methods are discussed. Some theoretical results are established to justify the use of sPCA-rSVD when only the data covariance matrix is available. In addition, we give a modified definition of variance explained by the sparse PCs. The sPCA-rSVD provides a uniform treatment of both classical multivariate data and high-dimension-low-sample-size (HDLSS) data. Further understanding of sPCA-rSVD and some existing alternatives is gained through simulation studies and real data examples, which suggests that sPCA-rSVD provides competitive results. We study the sparsity and optimality properties of crowd navigation and find that existing techniques do not satisfy both criteria simultaneously: either they achieve optimality with a prohibitive number of samples or tractability assumptions make them fragile to catastrophe. For example, if the human and robot are modeled independently, then tractability is attained but the planner is prone to overcautious or overaggressive behavior. For sampling based motion planning of joint human-robot cost functions, for @math agents and @math step lookahead, @math samples are needed for coverage of the action space. Advanced approaches statically partition the action space into free-space and then sample in those convex regions. However, if the human is into free-space, then the partition is misleading and sampling is unsafe: free space will soon be occupied. We diagnose the cause of these deficiencies---optimization happens over space---and propose a novel solution: optimize over trajectory space by using a Gaussian process (GP) basis. We exploit the "kernel trick" of GPs, where a continuum of trajectories are captured with a mean and covariance function. By using the mean and covariance as proxies for a trajectory family we reason about collective trajectory behavior without resorting to sampling. The GP basis is sparse and optimal with respect to collision avoidance and robot and crowd intention and flexibility. GP sparsity leans heavily on the insight that joint action space decomposes into free regions; however, the decomposition contains feasible solutions only if the partition is dynamically generated. We call our approach . The analysis and understanding of video sequences is currently quite an active research field. Many applications such as video surveillance, optical motion capture or those of multimedia need to first be able to detect the objects moving in a scene filmed by a static camera. This requires the basic operation that consists of separating the moving objects called "foreground" from the static information called "background". Many background subtraction methods have been developed ( (2010); (2008)). A recent survey (Bouwmans (2009)) shows that subspace learning models are well suited for background subtraction. Principal Component Analysis (PCA) has been used to model the background by significantly reducing the data's dimension. To perform PCA, different Robust Principal Components Analysis (RPCA) models have been recently developed in the literature. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. However, authors compare their algorithm only with the PCA ( (1999)) or another RPCA model. Furthermore, the evaluation is not made with the datasets and the measures currently used in the field of background subtraction. Considering all of this, we propose to evaluate RPCA models in the field of video-surveillance. Contributions of this chapter can be summarized as follows: 1) A survey regarding robust principal component analysis and 2) An evaluation and comparison on different video surveillance datasets We study the problem of multimodal dimensionality reduction assuming that data samples can be missing at training time, and not all data modalities may be present at application time. Maximum covariance analysis, as a generalization of PCA, has many desirable properties, but its application to practical problems is limited by its need for perfectly paired data. We overcome this limitation by a latent variable approach that allows working with weakly paired data and is still able to efficiently process large datasets using standard numerical routines. The resulting weakly paired maximum covariance analysis often finds better representations than alternative methods, as we show in two exemplary tasks: texture discrimination and transfer learning. This paper addresses the task of road safety assessment. An emerging approach for conducting such assessments in the United States is through the US Road Assessment Program (usRAP), which rates roads from highest risk (1 star) to lowest (5 stars). Obtaining these ratings requires manual, fine-grained labeling of roadway features in streetlevel panoramas, a slow and costly process. We propose to automate this process using a deep convolutional neural network that directly estimates the star rating from a street-level panorama, requiring milliseconds per image at test time. Our network also estimates many other roadlevel attributes, including curvature, roadside hazards, and the type of median. To support this, we incorporate taskspecific attention layers so the network can focus on the panorama regions that are most useful for a particular task. We evaluated our approach on a large dataset of real-world images from two US states. We found that incorporating additional tasks, and using a semi-supervised training approach, significantly reduced overfitting problems, allowed us to optimize more layers of the network, and resulted in higher accuracy. A method for efficient border ownership assignment in 2D images is proposed. Leveraging on recent advances using Structured Random Forests (SRF) for boundary detection [8], we impose a novel border ownership structure that detects both boundaries and border ownership at the same time. Key to this work are features that predict ownership cues from 2D images. To this end, we use several different local cues: shape, spectral properties of boundary patches, and semi-global grouping cues that are indicative of perceived depth. For shape, we use HoG-like descriptors that encode local curvature (convexity and concavity). For spectral properties, such as extremal edges [28], we first learn an orthonormal basis spanned by the top K eigenvectors via PCA over common types of contour tokens [23]. For grouping, we introduce a novel mid-level descriptor that captures patterns near edges and indicates ownership information of the boundary. Experimental results over a subset of the Berkeley Segmentation Dataset (BSDS) [24] and the NYU Depth V2 [34] dataset show that our method's performance exceeds current state-of-the-art multi-stage approaches that use more complex features. Given a set of images containing multiple object categories, we seek to discover those categories and their image locations without supervision. We achieve this using generative models from the statistical text literature: probabilistic Latent Semantic Analysis (pLSA), and Latent Dirichlet Allocation (LDA). In text analysis these are used to discover topics in a corpus using the bag-of-words document representation. Here we discover topics as object categories, so that an image containing instances of several categories is modelled as a mixture of topics. The models are applied to images by using a visual analogue of a word, formed by vector quantizing SIFT like region descriptors. We investigate a set of increasingly demanding scenarios, starting with image sets containing only two object categories through to sets containing multiple categories (including airplanes, cars, faces, motorbikes, spotted cats) and background clutter. The object categories sample both intra-class and scale variation, and both the categories and their approximate spatial layout are found without supervision. We also demonstrate classification of unseen images and images containing multiple objects. Performance of the proposed unsupervised method is compared to the semi-supervised approach of [7].1 1This work was sponsored in part by the EU Project CogViSys, the University of Oxford, Shell Oil, and the National Geospatial-Intelligence Agency. Many state-of-the-art approaches for object recognition reduce the problem to a 0-1 classification task. This allows one to leverage sophisticated machine learning techniques for training classifiers from labeled examples. However, these models are typically trained independently for each class using positive and negative examples cropped from images. At test-time, various post-processing heuristics such as non-maxima suppression (NMS) are required to reconcile multiple detections within and between different classes for each image. Though crucial to good performance on benchmarks, this post-processing is usually defined heuristically. We introduce a unified model for multi-class object recognition that casts the problem as a structured prediction task. Rather than predicting a binary label for each image window independently, our model simultaneously predicts a structured labeling of the entire image (Fig. 1). Our model learns statistics that capture the spatial arrangements of various object classes in real images, both in terms of which arrangements to suppress through NMS and which arrangements to favor through spatial co-occurrence statistics. We formulate parameter estimation in our model as a max-margin learning problem. Given training images with ground-truth object locations, we show how to formulate learning as a convex optimization problem. We employ the cutting plane algorithm of (Mach. Learn. 2009) to efficiently learn a model from thousands of training images. We show state-of-the-art results on the PASCAL VOC benchmark that indicate the benefits of learning a global model encapsulating the spatial layout of multiple object classes (a preliminary version of this work appeared in ICCV 2009, , IEEE international conference on computer vision, 2009).