Related papers: Learning Fractals by Gradient Descent

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

The topic of semantic segmentation has witnessed considerable progress due to the powerful features learned by convolutional neural networks (CNNs). The current leading approaches for semantic segmentation exploit shape information by…

We examine the optical properties of a system of nano and micro particles of varying size, shape, and material (including metals and dielectrics, and sub-wavelength and super-wavelength regimes). Training data is generated by numerically…

Adaptive control achieves concurrent parameter learning and stable control under uncertainties that are linearly parameterized with known nonlinear features. Nonetheless, it is often difficult to obtain such nonlinear features. To address…

Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…

In this paper, we propose to exploit the rich hierarchical features of deep convolutional neural networks to improve the accuracy and robustness of visual tracking. Deep neural networks trained on object recognition datasets consist of…

This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…

We propose PartField, a feedforward approach for learning part-based 3D features, which captures the general concept of parts and their hierarchy without relying on predefined templates or text-based names, and can be applied to open-world…

Dictionary learning is a versatile method to produce an overcomplete set of vectors, called atoms, to represent a given input with only a few atoms. In the literature, it has been used primarily for tasks that explore its powerful…

Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered…

We propose a new method for fine-grained few-shot recognition via deep object parsing. In our framework, an object is made up of K distinct parts and for each part, we learn a dictionary of templates, which is shared across all instances…

Sparse coding is a common approach to learning local features for object recognition. Recently, there has been an increasing interest in learning features from spatio-temporal, binocular, or other multi-observation data, where the goal is…

The task of shape abstraction with semantic part consistency is challenging due to the complex geometries of natural objects. Recent methods learn to represent an object shape using a set of simple primitives to fit the target.…

Pursuing realistic results according to human visual perception is the central concern in the image transformation tasks. Perceptual learning approaches like perceptual loss are empirically powerful for such tasks but they usually rely on…

We present a novel approach to background subtraction that is based on the local shape of small image regions. In our approach, an image region centered on a pixel is mod-eled using the local self-similarity descriptor. We aim at obtaining…

Reconstructing an object's geometry and appearance from multiple images, also known as inverse rendering, is a fundamental problem in computer graphics and vision. Inverse rendering is inherently ill-posed because the captured image is an…

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…

Due to the current lack of large-scale datasets at the million-scale level, tasks involving panoramic images predominantly rely on existing two-dimensional pre-trained image benchmark models as backbone networks. However, these networks are…

Artificial objects usually have very stable shape features, which are stable, persistent properties in geometry. They can provide evidence for object recognition. Shape features are more stable and more distinguishing than appearance…

In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This…