Online task-free continual learning requires models to learn from a non-stationary data stream without task boundaries, replay buffers, or multiple passes, while preserving previously acquired knowledge. Existing exemplar-free methods either rely on unstable geometric assumptions or synthetic feature generation, which may degrade under highly non-stationary streams. To address these limitations, we propose GCHP, a Geometry-Controlled Convex Hull Prototype Framework with adaptive structure control for online task-free continual learning. GCHP represents each class by maintaining a convex hull in a low-dimensional control space, together with its corresponding semantic prototypes in the original feature space. Upon receiving new samples, the hull is updated via expansion and contraction in the control space, and regulated prototypes are embedded into the original feature space for inference. This geometry-controlled mechanism enables stable boundary refinement under bounded prototype capacity without storing real exemplars. Extensive experiments on CIFAR-10, CIFAR-100, CORe-50, and CUB-200 show that GCHP achieves strong performance across benchmarks, despite operating in a strictly single-pass setting without using memory buffers. GCHP achieves competitive or superior performance compared to prior approaches across multiple benchmarks, outperforming existing methods on several datasets while remaining competitive on more challenging fine-grained scenarios such as CUB-200. Ablation studies further demonstrate the importance of the geometric representation and the robustness of the prototype capacity. These results underline the effectiveness of geometric consolidation for continual learning and highlight GCHP as a simple, stable, and scalable alternative for online exemplar-free scenarios. The code implementation of the proposed GCHP framework is available at https://github.com/tutc/GCHP .

A novel method for detecting rotational symmetry is addressed in this paper by introducing a new concept of semi-shapes to overcome the main problem of projection-based approaches for studying rotational symmetric properties of an arbitrary shape. It is due to the fact that in the classical approaches, projection cues are periodical with a period of π preventing exploitation of rotational properties. We then propose the profile of semi-shapes as a signature of the shape together with a simple yet efficient technique to determine the rotation symmetry of an arbitrary shape by considering the correlation of this signature and its circular shift. A new measure is also introduced to determine how good the rotational symmetry would be. Experiments on single/compound-contour shapes have clearly corroborated the efficacy of our proposal.

We present two novel shape signature-based reflection symmetry detection methods with their theoretical underpinning and empirical evaluation. LIP-signature and R-signature share similar beneficial properties allowing to detect reflection symmetry directions in a high-performing manner. For the shape signature of a given shape, its merit profile is constructed to detect candidates of symmetry direction. A verification process is utilized to eliminate the false candidates by addressing Radon projections. The proposed methods can effectively deal with compound shapes which are challenging for traditional contour-based methods. To quantify the symmetric efficiency, a new symmetry measure is proposed over the range [0, 1]. Furthermore, we introduce two symmetry shape datasets with a new evaluation protocol and a lost measure for evaluating symmetry detectors. Experimental results using standard and new datasets suggest that the proposed methods prominently perform compared to state of the art.

Understanding dynamic textures (DTs) is a challenge in various computer vision applications due to the negative impacts of noise, changes of environment, illumination, and scales on capturing turbulent characteristics. In this work, we propose an efficient shallow framework for DT representation by addressing the following novel concepts. First, it is the first time in DT analysis that 2D/3D Gaussian-gradient filterings are taken into account as a pre-processing step to point out robust components against those influences in effect. Second, high-order partial derivatives of the Gaussian kernels and their informative magnitudes are exploited to forcefully capture multi-order Gaussian-gradient features. Third, these gradient kernels are investigated in multi-scale analysis of different orders and standard deviations in order to enrich more useful scale-gradient information. Finally, the obtained complementary components are shallowly encoded using a simple local operator to construct robust descriptors of High-order 2D/3D Gaussian-gradient-based Features ($\mathrm{HoGF}^{2D/3D}$) against the well-known issues of DT description. Experiments for DT classification on various benchmarks have validated the interest of our approach since its performance is comparable to state-of-the-art results, including that of deep-learning methods, while it only has a small dimension.

Representation of dynamic textures (DTs), well‐known as a sequence of moving textures, is a challenging problem in video analysis due to the disorientation of motion features. Analysing DTs to make them ‘understandable’ plays an important role in different applications of computer vision. In this study, an efficient approach for DT description is proposed by addressing the following novel concepts. First, the beneficial properties of dense trajectories are exploited for the first time to efficiently describe DTs instead of the whole video. Second, two substantial extensions of local vector pattern operator are introduced to form a completed model which is based on complemented components to enhance its performance in encoding directional features of motion points in a trajectory. Finally, the authors present a new framework, called directional dense trajectory patterns, which takes advantage of directional beams of dense trajectories along with spatio‐temporal features of their motion points in order to construct dense‐trajectory‐based descriptors with more robustness. Evaluations of DT recognition on different benchmark datasets (i.e. UCLA, DynTex, and DynTex++) have verified the interest of the authors’ proposal.

An efficient framework for dynamic texture (DT) representation is proposed by exploiting local features based on Local Binary Patterns (LBP) from filtered images. First, Gaussian smoothing filter is used to deal with near uniform regions and noise which are typical restrictions of LBP operator. Second, the receptive field of Difference of Gaussians (DoG), which is exploited in DT description for the first time, allows to make the descriptor more robust against the changes of environment, illumination, and scale which are main challenges in DT representation. Experimental results of DT recognition on different benchmark datasets (i.e., UCLA, DynTex, and DynTex++), which give outstanding performance compared to the state of the art, verify the interest of our proposal.