In this paper, we introduce a novel framework for memory-efficient and privacy-preserving continual learning in 3D object classification. Unlike conventional memory-based approaches in continual learning that require storing numerous exemplars, our method constructs a compact shape model for each class, retaining only the mean shape along with a few key modes of variation. This strategy not only enables the generation of diverse training samples while drastically reducing memory usage but also enhances privacy by eliminating the need to store original data. To further improve model robustness against input variations—an issue common in 3D domains due to the absence of strong backbones and limited training data—we incorporate Gradient Mode Regularization. This technique enhances model stability and broadens classification margins, resulting in accuracy improvements. We validate our approach through extensive experiments on the ModelNet40, ShapeNet, and ScanNet datasets, where we achieve state-of-the-art performance. Notably, our method consumes only 15% of the memory required by competing methods on the ModelNet40 and ShapeNet, while achieving comparable performance on the challenging ScanNet dataset with just 8.5% of the memory. These results underscore the scalability, effectiveness, and privacy-preserving strengths of our framework for 3D object classification.

We introduce a novel framework for continual learning in 3D object classification. Our approach, CL3D, is based on the selection of prototypes from each class using spectral clustering. For non-Euclidean data such as point clouds, spectral clustering can be employed as long as one can define a distance measure between pairs of samples. Choosing the appropriate distance measure enables us to leverage 3D geometric characteristics to identify representative prototypes for each class. We explore the effectiveness of clustering in the input space (3D points), local feature space (1024-dimensional points), and global feature space. We conduct experiments on the ModelNet40, ShapeNet, and ScanNet datasets, achieving state-of-the-art accuracy exclusively through the use of input space features. By leveraging the combined input, local, and global features, we have improved the state-of-the-art on ModelNet and ShapeNet, utilizing nearly half the memory used by competing approaches. For the challenging ScanNet dataset, our method enhances accuracy by 4.1 % while consuming just 28 % of the memory used by our competitors, demonstrating the scalability of our approach. 1Project page: https://doollakh.github.io/cl3d/

We study the relation between the correlation-based target functions of low-resolution and high-resolution intensity-based registration for the class of rigid transformations. Our results show that low-resolution target values can tightly bound the high-resolution target function in natural images. This can help with analyzing and better understanding the process of multiresolution image registration. It also gives a guideline for designing multiresolution algorithms in which the search space in higher resolution registration is restricted given the fitness values for lower resolution image pairs. To demonstrate this, we incorporate our multiresolution technique into a Lipschitz global optimization framework. We show that using the multiresolution scheme can result in large gains in the efficiency of such algorithms. The method is evaluated by applying to the problems of 2D registration, 3D rotation search, and the detection of reflective symmetry in 2D and 3D images.

High computational cost is the main obstacle to adapting globally optimal branch-and-bound algorithms to intensity-based registration. Existing techniques to speed up such algorithms use a multiresolution pyramid of images and bounds on the target function among different resolutions for rigidly aligning two images. In this paper, we propose a dual algorithm in which the optimization is done in the Fourier domain, and multiple resolution levels are replaced by multiple frequency bands. The algorithm starts by computing the target function in lower frequency bands and keeps adding higher frequency bands until the current subregion is either rejected or divided into smaller areas in a branch and bound manner. Unlike spatial multiresolution approaches, to compute the target function for a wider frequency area, one just needs to compute the target in the residual bands. Therefore, if an area is to be discarded, it performs just enough computations required for the rejection. This property also enables us to use a rather large number of frequency bands compared to the limited number of resolution levels used in the space domain algorithm. Experimental results on real images demonstrate considerable speed gains over the space domain method in most cases.

We study the theory of projective reconstruction for multiple projections from an arbitrary dimensional projective space into lower-dimensional spaces. This problem is important due to its applications in the analysis of dynamical scenes. The current theory, due to Hartley and Schaffalitzky, is based on the Grassmann tensor, generalizing the ideas of fundamental matrix, trifocal tensor and quadrifocal tensor used in the well-studied case of 3D to 2D projections. We present a theory whose point of departure is the projective equations rather than the Grassmann tensor. This is a better fit for the analysis of approaches such as bundle adjustment and projective factorization which seek to directly solve the projective equations. In a first step, we prove that there is a unique Grassmann tensor corresponding to each set of image points, a question that remained open in the work of Hartley and Schaffalitzky. Then, we prove that projective equivalence follows from the set of projective equations given certain conditions on the estimated camera-point setup or the estimated projective depths. Finally, we demonstrate how wrong solutions to the projective factorization problem can happen, and classify such degenerate solutions based on the zero patterns in the estimated depth matrix.

Sparse Subspace Clustering (SSC) is one of the recent approaches to subspace segmentation. In SSC a graph is constructed whose nodes are the data points and whose edges are inferred from the L1-sparse representation of each point by the others. It has been proved that if the points lie on a mixture of independent subspaces, the graphical structure of each subspace is disconnected from the others. However, the problem of connectivity within each subspace is still unanswered. This is important since the subspace segmentation in SSC is based on finding the connected components of the graph. Our analysis is built upon the connection between the sparse representation through L1-norm minimization and the geometry of convex poly-topes proposed by the compressed sensing community. After introduction of some assumptions to make the problem well-defined, it is proved that the connectivity within each subspace holds for 2- and 3-dimensional subspaces. The claim of connectivity for general d-dimensional case, even for generic configurations, is proved false by giving a counterexample in dimensions greater than 3.

Braille is the most common means of reading and study for visually handicapped people. The need for converting Braille documents into a computer-readable format has motivated research into the implementation of Braille recognition systems. The most fundamental steps in such recognition are estimating the scaling, spacing, and skewness properties of a given Braille document. In this paper we propose a statistical method for estimating these parameters, where we model an entire Braille image using a parameterized probability density function and find the maximum-likelihood (ML) estimates using Expectation-Maximization (EM) algorithm. The proposed method is robust against noise and other image artifacts, and has a modest computational complexity for straightforward execution on ordinary personal computers.