arXiv subjects

Jesus Angulo

Publications and source records attributed to Jesus Angulo.

23 records · Page 2Linked to original sources

arXiv2019

Part-based approximations for morphological operators using asymmetric auto-encoders

This paper addresses the issue of building a part-based representation of a dataset of images. More precisely, we look for a non-negative, sparse decomposition of the images on a reduced set of atoms, in order to unveil a morphological and interpretable structure of the data. Additionally, we want this decomposition to be computed online for any new sample that is not part of the initial dataset. Therefore, our solution relies on a sparse, non-negative auto-encoder where the encoder is deep (for accuracy) and the decoder shallow (for interpretability). This method compares favorably to the state-of-the-art online methods on two datasets (MNIST and Fashion MNIST), according to classical metrics and to a new one we introduce, based on the invariance of the representation to morphological dilation.

cs.CV↗

arXiv2018

Regression and Classification by Zonal Kriging

Consider a family $Z=\{\boldsymbol{x_{i}},y_{i}$,$1\leq i\leq N\}$ of $N$ pairs of vectors $\boldsymbol{x_{i}} \in \mathbb{R}^d$ and scalars $y_{i}$ that we aim to predict for a new sample vector $\mathbf{x}_0$. Kriging models $y$ as a sum of a deterministic function $m$, a drift which depends on the point $\boldsymbol{x}$, and a random function $z$ with zero mean. The zonality hypothesis interprets $y$ as a weighted sum of $d$ random functions of a single independent variables, each of which is a kriging, with a quadratic form for the variograms drift. We can therefore construct an unbiased estimator $y^{*}(\boldsymbol{x_{0}})=\sum_{i}λ^{i}z(\boldsymbol{x_{i}})$ de $y(\boldsymbol{x_{0}})$ with minimal variance $E[y^{*}(\boldsymbol{x_{0}})-y(\boldsymbol{x_{0}})]^{2}$, with the help of the known training set points. We give the explicitly closed form for $λ^{i}$ without having calculated the inverse of the matrices.

stat.ML↗

arXiv2016

Hyperspectral Image Classification with Support Vector Machines on Kernel Distribution Embeddings

We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions -- by representing them with mean elements in reproducing kernel Hilbert spaces (RKHS) and formulating a classification algorithm therein. In particular, we associate each pixel to an empirical distribution of its neighbouring pixels, a judicious representation of which in an RKHS, in conjunction with the spectral information contained in the pixel itself, give a new explicit set of features that can be fed into a suite of standard classification techniques -- we opt for a well-established framework of support vector machines (SVM). Furthermore, the computational complexity is reduced via random Fourier features formalism. We study the consistency and the convergence rates of the proposed method and the experiments demonstrate strong performance on hyperspectral data with gains in comparison to the state-of-the-art results.

cs.CV↗

arXiv2016

A New Spatio-Spectral Morphological Segmentation For Multi-Spectral Remote-Sensing Images

A general framework of spatio-spectral segmentation for multi-spectral images is introduced in this paper. The method is based on classification-driven stochastic watershed (WS) by Monte Carlo simulations, and it gives more regular and reliable contours than standard WS. The present approach is decomposed into several sequential steps. First, a dimensionality-reduction stage is performed using the factor-correspondence analysis method. In this context, a new way to select the factor axes (eigenvectors) according to their spatial information is introduced. Then, a spectral classification produces a spectral pre-segmentation of the image. Subsequently, a probability density function (pdf) of contours containing spatial and spectral information is estimated by simulation using a stochastic WS approach driven by the spectral classification. The pdf of the contours is finally segmented by a WS controlled by markers from a regularization of the initial classification.

cs.CV↗

arXiv2016

On distances, paths and connections for hyperspectral image segmentation

The present paper introduces the $η$ and η connections in order to add regional information on $λ$-flat zones, which only take into account a local information. A top-down approach is considered. First $λ$-flat zones are built in a way leading to a sub-segmentation. Then a finer segmentation is obtained by computing $η$-bounded regions and $μ$-geodesic balls inside the $λ$-flat zones. The proposed algorithms for the construction of new partitions are based on queues with an ordered selection of seeds using the cumulative distance. $η$-bounded regions offers a control on the variations of amplitude in the class from a point, called center, and $μ$-geodesic balls controls the "size" of the class. These results are applied to hyperspectral images.

cs.CV↗