Sparse Subspace Clustering in Hyperspectral Images using Incomplete Pixels

El agrupamiento de imágenes espectrales es un método de clasificación no supervisada que identifica las distribuciones de píxeles utilizando información espectral sin necesidad de una etapa previa de entrenamiento. Los métodos basados ​​en agrupación de subespacio escasos (SSC) suponen que las imágenes hiperespectrales viven en la unión de múltiples subespacios de baja dimensión. Basado en esto, SSC asigna firmas espectrales a diferentes subespacios, expresando cada firma espectral como una combinación lineal escasa de todos los píxeles, garantizando que los elementos que no son cero pertenecen a la misma clase. Aunque estos métodos han demostrado una buena precisión para la clasificación no supervisada de imágenes hiperespectrales, a medida que aumenta el número de píxeles, es decir, la dimensión de la imagen es grande, la complejidad computacional se vuelve intratable. Por este motivo, este documento propone reducir el número de píxeles a clasificar en la imagen hiperespectral, y posteriormente, los resultados del agrupamiento para los píxeles faltantes se obtienen explotando la información espacial. Específicamente, este trabajo propone dos metodologías para remover los píxeles, la primera se basa en una distribución espacial de ruido azul que reduce la probabilidad de que se eliminen píxeles vecinos y la segunda es un procedimiento de submuestreo que elimina cada dos píxeles contiguos, preservando la estructura espacial de la escena. El rendimiento del algoritmo de agrupamiento de imágenes espectrales propuesto se evalúa en tres conjuntos de datos mostrando que se obtiene una precisión similar cuando se elimina hasta la mitad de los pixeles, además, es hasta 7.9 veces más rápido en comparación con la clasificación de los conjuntos de datos completos.Spectral image clustering is an unsupervised classification method which identifies distributions of pixels using spectral information without requiring a previous training stage. The sparse subspace clustering-based methods (SSC) assume that hyperspectral images lie in the union of multiple low-dimensional subspaces.  Using this, SSC groups spectral signatures in different subspaces, expressing each spectral signature as a sparse linear combination of all pixels, ensuring that the non-zero elements belong to the same class. Although these methods have shown good accuracy for unsupervised classification of hyperspectral images, the computational complexity becomes intractable as the number of pixels increases, i.e. when the spatial dimension of the image is large. For this reason, this paper proposes to reduce the number of pixels to be classified in the hyperspectral image, and later, the clustering results for the missing pixels are obtained by exploiting the spatial information. Specifically, this work proposes two methodologies to remove the pixels, the first one is based on spatial blue noise distribution which reduces the probability to remove cluster of neighboring pixels, and the second is a sub-sampling procedure that eliminates every two contiguous pixels, preserving the spatial structure of the scene. The performance of the proposed spectral image clustering framework is evaluated in three datasets showing that a similar accuracy is obtained when up to 50% of the pixels are removed, in addition, it is up to 7.9 times faster compared to the classification of the data sets without incomplete pixels

Fast Disparity Estimation from a Single Compressed Light Field Measurement

The abundant spatial and angular information from light fields has allowed the development of multiple disparity estimation approaches. However, the acquisition of light fields requires high storage and processing cost, limiting the use of this technology in practical applications. To overcome these drawbacks, the compressive sensing (CS) theory has allowed the development of optical architectures to acquire a single coded light field measurement. This measurement is decoded using an optimization algorithm or deep neural network that requires high computational costs. The traditional approach for disparity estimation from compressed light fields requires first recovering the entire light field and then a post-processing step, thus requiring long times. In contrast, this work proposes a fast disparity estimation from a single compressed measurement by omitting the recovery step required in traditional approaches. Specifically, we propose to jointly optimize an optical architecture for acquiring a single coded light field snapshot and a convolutional neural network (CNN) for estimating the disparity maps. Experimentally, the proposed method estimates disparity maps comparable with those obtained from light fields reconstructed using deep learning approaches. Furthermore, the proposed method is 20 times faster in training and inference than the best method that estimates the disparity from reconstructed light fields

Computational Spectral Imaging: A Contemporary Overview

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow identifying objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire the 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where the 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared to conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarises the advances in CSI, starting with SI and its relevance; continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, and the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks

Classification of Hass avocado (persea americana mill) in terms of its ripening via hyperspectral images

El uso de metodologías no invasivas y de bajo costo permiten el seguimiento de la madurez y calidad de los frutos, sin afectar el producto bajo estudio. En particular, el aguacate Hass es de alta importancia para el sector agrícola en Colombia, ya que se está impulsando fuertemente su exportación, generando una expansión del terreno cultivado con este fruto. Por consiguiente, en este artículo se estudia y analiza el estado de madurez del aguacate Hass, a través de un sistema de captura de imágenes hiperespectrales no-invasivo, utilizando técnicas de análisis de componentes principales (PCA), realizando seguimiento por medio del índice de vegetación de diferencia normalizada (NDVI), el índice de vegetación de relación  (RVI) y el índice de reflectancia fotoquímica (PRI) e índices de colorimetría en el espacio de color CIE L*a*b* y el índice de verdor triangular (TGI). En particular, en este trabajo se realizó un análisis cuantitativo del proceso de maduración con una población de 7 aguacates a lo largo de 10 días, los cuales fueron clasificados a través de tres categorías: verdes, próximos a madurar y maduros. Los resultados obtenidos muestran que es posible caracterizar los aguacates por medio de imágenes hiperespectrales, utilizando un sistema de adquisición no invasivo. Con este análisis se espera poder clasificar una producción de aguacates en cualquier día de la post-cosecha.The use of non-invasive and low-cost methodologies allows the monitoring of fruit ripening and quality control, without affecting the product under study. In particular, the Hass avocado is of high importance for the agricultural sector in Colombia because the country is strongly promoting its export, which has generated an expansion in the number of acres cultivated with this fruit. Therefore, this paper aims to study and analyze the ripening state of Hass avocados through non-invasive hyperspectral images, using principal component analysis (PCA) along with spectral vegetation indices, such as the normalized difference vegetation index (NDVI), ratio vegetation index (RVI), photochemical reflectance index (PRI), colorimetry analysis in the CIE L*a*b* color space, and color index triangular greenness index (TGI). In particular, this work conducts a quantitative analysis of the ripening process of a population of 7 Hass avocados over 10 days. The avocados under study were classified into three categories: unripe, close-to-ripe, and ripe. The obtained results show that it is possible to characterize the ripening state of avocados through hyperspectral images using a non-invasive acquisition system. Further, it is possible to know the post-harvest ripening state of the avocado at any given day

Mixture-Net: Low-Rank Deep Image Prior Inspired by Mixture Models for Spectral Image Recovery

This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the proposed approach, dubbed Mixture-Net, implicitly learns the prior information through the network. Mixture-Net consists of a deep generative model whose layers are inspired by the linear and non-linear low-rank mixture models, where the recovered image is composed of a weighted sum between the linear and non-linear decomposition. Mixture-Net also provides a low-rank decomposition interpreted as the spectral image abundances and endmembers, helpful in achieving remote sensing tasks without running additional routines. The experiments show the MixtureNet effectiveness outperforming state-of-the-art methods in recovery quality with the advantage of architecture interpretability

Spectral unmixing approach in hyperspectral remote sensing: a tool for oil palm mapping

Las plantaciones de palma de aceite típicamente abarcan grandes áreas, por esto, la teledetección remota se ha convertido en una herramienta útil para el monitoreo avanzado de este cultivo. Este trabajo revisa y evalúa dos enfoques para analizar las plantaciones de palma de aceite a partir de datos de teledetección remota hiperespectral: desmezclado espectral lineal y variabilidad espectral. Además, se propone un marco computacional basado en el desmezclado espectral para la estimación de las fracciones de abundancias de cultivos de palma de aceite. Este enfoque también considera la variabilidad espectral de las firmas en las imágenes hiperespectrales. El marco computacional propuesto modifica el modelo de mezcla lineal mediante la introducción de un vector de pesos, de manera que se puedan identificar las bandas espectrales que menos contribuyen a la estimación de fracciones de abundancias erróneas. Este enfoque aprovecha la detección de los árboles de palma de aceite, ya que permite diferenciarlos de otros materiales en términos de fracciones de abundancia. Los resultados experimentales obtenidos a partir de datos de teledetección remota hiperespectral en el rango de 410-990 nm, muestran mejoras de un 8.18 % en la métrica de Precisión del Usuario (Uacc) en la identificación de palmas de aceite por el marco propuesto con respecto a los métodos tradicionales de desmezclado espectral; el método propuesto logró un 95 % de Uacc. Esto confirma las capacidades del marco computacional formulado y facilita la gestión y el monitoreo de grandes áreas de plantaciones de palma de aceite.Oil palm plantations typically span large areas; therefore, remote sensing has become a useful tool for advanced oil palm monitoring. This work reviews and evaluates two approaches to analyze oil palm plantations based on hyperspectral remote sensing data: linear spectral unmixing and spectral variability. Moreover, a computational framework based on spectral unmixing for the estimation of fractional abundances of oil palm plantations is proposed in this study. Such approach also considers the spectral variability of hyperspectral image signatures. More specifically, the proposed computational framework modifies the linear mixing model by introducing a weighting vector, so that the spectral bands that contribute the least to the estimation of erroneous fractional abundances can be identified. This approach improves palm detection as it allows to differentiate them from other materials in terms of fractional abundances. Experimental results obtained from hyperspectral remote sensing data in the range 410-990 nm show improvements of 8.18 % in User Accuracy (Uacc) in the identification of oil palms by the proposed framework with respect to traditional unmixing methods. Thus, the proposed method achieved a 95% Uacc. This confirms the capabilities of the proposed computational framework and facilitates the management and monitoring of large areas of oil palm plantations

Sistemas de reconocimiento basados en la imagen facial

Este artículo sintetiza las principales investigaciones que se están llevando a cabo en el área de los sistemas de reconocimiento a través de la imagen facial. Se realiza la descripción de las principales líneas de trabajo en los sistema de identificación de personas por medio de la imagen del rostro. Además, se realiza una síntesis de las últimas técnicas matemáticas para realizar la extracción de características dentro de estos sistemas de identificación

Covariance Estimation from Compressive Data Partitions using a Projected Gradient-based Algorithm

Covariance matrix estimation techniques require high acquisition costs that challenge the sampling systems' storing and transmission capabilities. For this reason, various acquisition approaches have been developed to simultaneously sense and compress the relevant information of the signal using random projections. However, estimating the covariance matrix from the random projections is an ill-posed problem that requires further information about the data, such as sparsity, low rank, or stationary behavior. Furthermore, this approach fails using high compression ratios. Therefore, this paper proposes an algorithm based on the projected gradient method to recover a low-rank or Toeplitz approximation of the covariance matrix. The proposed algorithm divides the data into subsets projected onto different subspaces, assuming that each subset contains an approximation of the signal statistics, improving the inverse problem's condition. The error induced by this assumption is analytically derived along with the convergence guarantees of the proposed method. Extensive simulations show that the proposed algorithm can effectively recover the covariance matrix of hyperspectral images with high compression ratios (8-15% approx) in noisy scenarios. Additionally, simulations and theoretical results show that filtering the gradient reduces the estimator's error recovering up to twice the number of eigenvectors.Comment: submitted to IEEE Transactions on Image Processin