Shape-Color Differential Moment Invariants under Affine Transformations

We propose the general construction formula of shape-color primitives by using partial differentials of each color channel in this paper. By using all kinds of shape-color primitives, shape-color differential moment invariants can be constructed very easily, which are invariant to the shape affine and color affine transforms. 50 instances of SCDMIs are obtained finally. In experiments, several commonly used color descriptors and SCDMIs are used in image classification and retrieval of color images, respectively. By comparing the experimental results, we find that SCDMIs get better results.Comment: 13 pages, 4 figure

Image Projective Invariants

In this paper, we propose relative projective differential invariants (RPDIs) which are invariant to general projective transformations. By using RPDIs and the structural frame of integral invariant, projective weighted moment invariants (PIs) can be constructed very easily. It is first proved that a kind of projective invariants exists in terms of weighted integration of images, with relative differential invariants as the weight functions. Then, some simple instances of PIs are given. In order to ensure the stability and discriminability of PIs, we discuss how to calculate partial derivatives of discrete images more accurately. Since the number of pixels in discrete images before and after the geometric transformation may be different, we design the method to normalize the number of pixels. These ways enhance the performance of PIs. Finally, we carry out some experiments based on synthetic and real image datasets. We choose commonly used moment invariants for comparison. The results indicate that PIs have better performance than other moment invariants in image retrieval and classification. With PIs, one can compare the similarity between images under the projective transformation without knowing the parameters of the transformation, which provides a good tool to shape analysis in image processing, computer vision and pattern recognition

Local Feature Detectors, Descriptors, and Image Representations: A Survey

With the advances in both stable interest region detectors and robust and distinctive descriptors, local feature-based image or object retrieval has become a popular research topic. %All of the local feature-based image retrieval system involves two important processes: local feature extraction and image representation. The other key technology for image retrieval systems is image representation such as the bag-of-visual words (BoVW), Fisher vector, or Vector of Locally Aggregated Descriptors (VLAD) framework. In this paper, we review local features and image representations for image retrieval. Because many and many methods are proposed in this area, these methods are grouped into several classes and summarized. In addition, recent deep learning-based approaches for image retrieval are briefly reviewed.Comment: 20 page

A Novel Space-Time Representation on the Positive Semidefinite Con for Facial Expression Recognition

In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the advantage to bring naturally a second desirable quantity when comparing shapes -- the spatial covariance -- in addition to the conventional affine-shape representation. We derive then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the manifold. Specifically, our approach involves three steps: 1) facial landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of rank 2, to build time-parameterized trajectories; 2) a temporal alignment is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; 3) finally, pairwise proximity function SVM (ppfSVM) is used to classify them, incorporating the latter (dis-)similarity measure into the kernel function. We show the effectiveness of the proposed approach on four publicly available benchmarks (CK+, MMI, Oulu-CASIA, and AFEW). The results of the proposed approach are comparable to or better than the state-of-the-art methods when involving only facial landmarks.Comment: To be appeared at ICCV 201

Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms

Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of potentially complicated microscopic crystal images, providing feedback to tweak theories and improve synthesis in materials science. As such, an efficient phase-space sketching method is proposed to encode microscopic crystal images in a translation, rotation, illumination, and scale invariant representation, which is also stable with respect to small deformations. Based on the phase-space sketching, we generalize our previous analysis framework for crystal images with simple structures to those with complicated geometry

From BoW to CNN: Two Decades of Texture Representation for Texture Classification

Texture is a fundamental characteristic of many types of images, and texture representation is one of the essential and challenging problems in computer vision and pattern recognition which has attracted extensive research attention. Since 2000, texture representations based on Bag of Words (BoW) and on Convolutional Neural Networks (CNNs) have been extensively studied with impressive performance. Given this period of remarkable evolution, this paper aims to present a comprehensive survey of advances in texture representation over the last two decades. More than 200 major publications are cited in this survey covering different aspects of the research, which includes (i) problem description; (ii) recent advances in the broad categories of BoW-based, CNN-based and attribute-based methods; and (iii) evaluation issues, specifically benchmark datasets and state of the art results. In retrospect of what has been achieved so far, the survey discusses open challenges and directions for future research.Comment: Accepted by IJC

Classification of curves in 2D and 3D via affine integral signatures

We propose a robust classification algorithm for curves in 2D and 3D, under the special and full groups of affine transformations. To each plane or spatial curve we assign a plane signature curve. Curves, equivalent under an affine transformation, have the same signature. The signatures introduced in this paper are based on integral invariants, which behave much better on noisy images than classically known differential invariants. The comparison with other types of invariants is given in the introduction. Though the integral invariants for planar curves were known before, the affine integral invariants for spatial curves are proposed here for the first time. Using the inductive variation of the moving frame method we compute affine invariants in terms of Euclidean invariants. We present two types of signatures, the global signature and the local signature. Both signatures are independent of parameterization (curve sampling). The global signature depends on the choice of the initial point and does not allow us to compare fragments of curves, and is therefore sensitive to occlusions. The local signature, although is slightly more sensitive to noise, is independent of the choice of the initial point and is not sensitive to occlusions in an image. It helps establish local equivalence of curves. The robustness of these invariants and signatures in their application to the problem of classification of noisy spatial curves extracted from a 3D object is analyzed.Comment: 30 pages, 16 figure

Partially Occluded Leaf Recognition via Subgraph Matching and Energy Optimization

We present an approach to match partially occluded plant leaves with databases of full plant leaves. Although contour based 2D shape matching has been studied extensively in the last couple of decades, matching occluded leaves with full leaf databases is an open and little worked on problem. Classifying occluded plant leaves is even more challenging than full leaf matching because of large variations and complexity of leaf structures. Matching an occluded contour with all the full contours in a database is an NP-hard problem [Su et al. ICCV2015], so our algorithm is necessarily suboptimal

Matching-Constrained Active Contours

In object segmentation by active contours, the initial contour is often required. Conventionally, the initial contour is provided by the user. This paper extends the conventional active contour model by incorporating feature matching in the formulation, which gives rise to a novel matching-constrained active contour. The numerical solution to the new optimization model provides an automated framework of object segmentation without user intervention. The main idea is to incorporate feature point matching as a constraint in active contour models. To this effect, we obtain a mathematical model of interior points to boundary contour such that matching of interior feature points gives contour alignment, and we formulate the matching score as a constraint to active contour model such that the feature matching of maximum score that gives the contour alignment provides the initial feasible solution to the constrained optimization model of segmentation. The constraint also ensures that the optimal contour does not deviate too much from the initial contour. Projected-gradient descent equations are derived to solve the constrained optimization. In the experiments, we show that our method is capable of achieving the automatic object segmentation, and it outperforms the related methods

Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old ones. Current augmentation schemes, however, rely on manual specification of the applied transformations, making data augmentation an implicit form of feature engineering. With an eye towards true end-to-end learning, we suggest learning the applied transformations on a per-class basis. Particularly, we align image pairs within each class under the assumption that the spatial transformation between images belongs to a large class of diffeomorphisms. We then learn a class-specific probabilistic generative models of the transformations in a Riemannian submanifold of the Lie group of diffeomorphisms. We demonstrate significant performance improvements in training deep neural nets over manually-specified augmentation schemes. Our code and augmented datasets are available online