Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifolds, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods

Revisiting Classical Multiclass Linear Discriminant Analysis with a Novel Prototype-based Interpretable Solution

Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical pattern recognition. For a dataset containing C clusters, the classical solution to LDA extracts at most C-1 features. Here, we introduce a novel solution to classical LDA, called LDA++, that yields C features, each interpretable as measuring similarity to one cluster. This novel solution bridges dimensionality reduction and multiclass classification. Specifically, we prove that, for homoscedastic Gaussian data and under some mild conditions, the optimal weights of a linear multiclass classifier also make an optimal solution to LDA. In addition, we show that LDA++ reveals some important new facts about LDA that remarkably changes our understanding of classical multiclass LDA after 75 years of its introduction. We provide a complete numerical solution for LDA++ for the cases 1) when the scatter matrices can be constructed explicitly, 2) when constructing the scatter matrices is infeasible, and 3) the kernel extension

A physically based trunk soft tissue modeling for scoliosis surgery planning systems

One of the major concerns of scoliotic patients undergoing spinal correction surgery is the trunk's external appearance after the surgery. This paper presents a novel incremental approach for simulating postoperative trunk shape in scoliosis surgery. Preoperative and postoperative trunk shapes data were obtained using three-dimensional medical imaging techniques for seven patients with adolescent idiopathic scoliosis. Results of qualitative and quantitative evaluations, based on the comparison of the simulated and actual postoperative trunk surfaces, showed an adequate accuracy of the method. Our approach provides a candidate simulation tool to be used in a clinical environment for the surgery planning process.IRSC / CIH

Binary Patterns Encoded Convolutional Neural Networks for Texture Recognition and Remote Sensing Scene Classification

Designing discriminative powerful texture features robust to realistic imaging conditions is a challenging computer vision problem with many applications, including material recognition and analysis of satellite or aerial imagery. In the past, most texture description approaches were based on dense orderless statistical distribution of local features. However, most recent approaches to texture recognition and remote sensing scene classification are based on Convolutional Neural Networks (CNNs). The d facto practice when learning these CNN models is to use RGB patches as input with training performed on large amounts of labeled data (ImageNet). In this paper, we show that Binary Patterns encoded CNN models, codenamed TEX-Nets, trained using mapped coded images with explicit texture information provide complementary information to the standard RGB deep models. Additionally, two deep architectures, namely early and late fusion, are investigated to combine the texture and color information. To the best of our knowledge, we are the first to investigate Binary Patterns encoded CNNs and different deep network fusion architectures for texture recognition and remote sensing scene classification. We perform comprehensive experiments on four texture recognition datasets and four remote sensing scene classification benchmarks: UC-Merced with 21 scene categories, WHU-RS19 with 19 scene classes, RSSCN7 with 7 categories and the recently introduced large scale aerial image dataset (AID) with 30 aerial scene types. We demonstrate that TEX-Nets provide complementary information to standard RGB deep model of the same network architecture. Our late fusion TEX-Net architecture always improves the overall performance compared to the standard RGB network on both recognition problems. Our final combination outperforms the state-of-the-art without employing fine-tuning or ensemble of RGB network architectures.Comment: To appear in ISPRS Journal of Photogrammetry and Remote Sensin