Polarimetric imaging of biological tissues based on the indices of polarimetric purity

Passive Polarized Vision for Autonomous Vehicles: A Review

This review article aims to address common research questions in passive polarized vision for robotics. What kind of polarization sensing can we embed into robots? Can we find our geolocation and true north heading by detecting light scattering from the sky as animals do? How should polarization images be related to the physical properties of reflecting surfaces in the context of scene understanding? This review article is divided into three main sections to address these questions, as well as to assist roboticists in identifying future directions in passive polarized vision for robotics. After an introduction, three key interconnected areas will be covered in the following sections: embedded polarization imaging; polarized vision for robotics navigation; and polarized vision for scene understanding. We will then discuss how polarized vision, a type of vision commonly used in the animal kingdom, should be implemented in robotics; this type of vision has not yet been exploited in robotics service. Passive polarized vision could be a supplemental perceptive modality of localization techniques to complement and reinforce more conventional ones.

Optimizing the classification of biological tissues using machine learning models based on polarized data

Polarimetric data is nowadays used to build recognition models for the characterization of organic tissues or the early detection of some diseases. Different Mueller matrix-derived polarimetric observables, which allow a physical interpretation of a specific characteristic of samples, are proposed in literature to feed the required recognition algorithms. However, they are obtained through mathematical transformations of the Mueller matrix and this process may loss relevant sample information in search of physical interpretation. In this work, we present a thorough comparative between 12 classification models based on different polarimetric datasets to find the ideal polarimetric framework to construct tissues classification models. The study is conducted on the experimental Mueller matrices images measured on different tissues: muscle, tendon, myotendinous junction and bone; from a collection of 165 ex-vivo chicken thighs. Three polarimetric datasets are analyzed: (A) a selection of most representative metrics presented in literature; (B) Mueller matrix elements; and (C) the combination of (A) and (B) sets. Results highlight the importance of using raw Mueller matrix elements for the design of classification models.

Automatic pseudo-coloring approaches to improve visual perception and contrast in polarimetric images of biological tissues

Imaging polarimetry methods have proved their suitability to enhance the image contrast between tissues and structures in organic samples, or even to reveal structures hidden in regular intensity images. These methods are nowadays used in a wide range of biological applications, as for the early diagnosis of different pathologies. To include the discriminatory potential of different polarimetric observables in a single image, a suitable strategy reported in literature consists in associating different observables to different color channels, giving rise to pseudo-colored images helping the visualization of different tissues in samples. However, previous reported polarimetric based pseudo-colored images of tissues are mostly based on simple linear combinations of polarimetric observables whose weights are set ad-hoc, and thus, far from optimal approaches. In this framework, we propose the implementation of two pseudo-colored methods. One is based on the Euclidean distances of actual values of pixels and an average value taken over a given region of interest in the considered image. The second method is based on the likelihood for each pixel to belong to a given class. Such classes being defined on the basis of a statistical model that describes the statistical distribution of values of the pixels in the considered image. The methods are experimentally validated on four different biological samples, two of animal origin and two of vegetal origin. Results provide the potential of the methods to be applied in biomedical and botanical applications.

Polarimetric observables for the enhanced visualization of plant diseases

This paper highlights the potential of using polarimetric methods for the inspection of plant diseased tissues. We show how depolarizing observables are a suitable tool for the accurate discrimination between healthy and diseased tissues due to the pathogen infection of plant samples. The analysis is conducted on a set of different plant specimens showing various disease symptoms and infection stages. By means of a complete image Mueller polarimeter, we measure the experimental Mueller matrices of the samples, from which we calculate a set of metrics analyzing the depolarization content of the inspected leaves. From calculated metrics, we demonstrate, in a qualitative and quantitative way, how depolarizing information of vegetal tissues leads to the enhancement of image contrast between healthy and diseased tissues, as well as to the revelation of wounded regions which cannot be detected by means of regular visual inspections. Moreover, we also propose a pseudo-colored image method, based on the depolarizing metrics, capable to further enhance the visual image contrast between healthy and diseased regions in plants. The ability of proposed methods to characterize plant diseases (even at early stages of infection) may be of interest for preventing yield losses due to different plant pathogens.

Urban objects classification using Mueller matrix polarimetry and machine learning

Detecting and recognizing different kinds of urban objects is an important problem, in particular, in autonomous driving. In this context, we studied the potential of Mueller matrix polarimetry for classifying a set of relevant real-world objects: vehicles, pedestrians, traffic signs, pavements, vegetation and tree trunks. We created a database with their experimental Mueller matrices measured at 1550 nm and trained two machine learning classifiers, support vector machine and artificial neural network, to classify new samples. The overall accuracy of over 95% achieved with this approach, with either models, reveals the potential of polarimetry, specially combined with other remote sensing techniques, to enhance object recognition.

Unraveling the physical information of depolarizers

The link between depolarization measures and physical nature and structure of material media inducing depolarization is nowadays an open question. This article shows how the joint use of two complementary sets of depolarizing metrics, namely the Indices of polarimetric purity and the Components of purity, are sufficient to completely describe the integral depolarizing properties of a sample. Based on a collection of illustrative and representative polarimetric configurations, a clear and meaningful physical interpretation of such metrics is provided, thus extending the current tools and comprehension for the study and analysis of the depolarizing properties of material media. This study could be of interest to those users dealing with depolarization or depolarizing samples.

Polarimetric data-based model for tissue recognition

We highlight the potential of a predictive optical model method for tissue recognition, based on the statistical analysis of different polarimetric indicators that retrieve complete polarimetric information (selective absorption, retardance and depolarization) of samples. The study is conducted on the experimental Mueller matrices of four biological tissues (bone, tendon, muscle and myotendinous junction) measured from a collection of 157 ex-vivo chicken samples. Moreover, we perform several non-parametric data distribution analyses to build a logistic regression-based algorithm capable to recognize, in a single and dynamic measurement, whether a sample corresponds (or not) to one of the four different tissue categories.

Customized depolarization spatial patterns with dynamic retardance functions

In this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid-crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase pattern. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

Histopathological correlations of bulk tissue polarimetric images: Case study

Polarimetric imaging and image analysis have gained increased interest in soft tissue analysis at the cellular level. However, polarimetric imaging has widely been tested on thin tissue sections to provide reliable information correlated with histopathological findings. Polarimetric bulk tissue analysis always offered an overall assessment of various tissue optical properties for diagnosis. In this study, the histopathological correlation of bulk tissue polarimetry images for soft tissues is discussed. The first-hand information on the use of bulk tissue Mueller polarimetry and image analysis as an alternative to tissue histopathology is presented for surgically extracted colon and breast tissues.

Measuring glucose concentration in a solution based on the indices of polarimetric purity

Polarization imaging is a powerful tool, which can be applied in biomedical diagnosis and many research fields. Here, we propose a new application of the indices of polarimetric purity (IPPs) composed of P1, P2, P3, to describe the glucose concentrations (GC) changes in the scattering system. The results suggest that P1 of the IPPs is a better indicator to GC in the solution than the degree of polarization (DoP) for the forward scattering detection. Meanwhile, the fitting relation among radius of scattering particle, GCs and P1 parameter has also been calculated, in which the error of inversion is no more than 4.73%. In the backscattering detection, the fitted frequency statistical histogram of the IPPs is used to measure the GCs, and their modes can represent changing trend of GCs.

Polarimetric imaging microscopy for advanced inspection of vegetal tissues

Optical microscopy techniques for plant inspection benefit from the fact that at least one of the multiple properties of light (intensity, phase, wavelength, polarization) may be modified by vegetal tissues. Paradoxically, polarimetric microscopy although being a mature technique in biophotonics, is not so commonly used in botany. Importantly, only specific polarimetric observables, as birefringence or dichroism, have some presence in botany studies, and other relevant metrics, as those based on depolarization, are underused. We present a versatile method, based on a representative selection of polarimetric observables, to obtain and to analyse images of plants which bring significant information about their structure and/or the spatial organization of their constituents (cells, organelles, among other structures). We provide a thorough analysis of polarimetric microscopy images of sections of plant leaves which are compared with those obtained by other commonly used microscopy techniques in plant biology. Our results show the interest of polarimetric microscopy for plant inspection, as it is non-destructive technique, highly competitive in economical and time consumption, and providing advantages compared to standard non-polarizing techniques.

Depolarization metric spaces for biological tissues classification

Classification of tissues is an important problem in biomedicine. An efficient tissue classification protocol allows, for instance, the guided-recognition of structures through treated images or discriminating between healthy and unhealthy regions (e.g., early detection of cancer). In this framework, we study the potential of some polarimetric metrics, the so-called depolarization spaces, for the classification of biological tissues. The analysis is performed using 120 biological ex vivo samples of three different tissues types. Based on these data collection, we provide for the first time a comparison between these depolarization spaces, as well as with most commonly used depolarization metrics, in terms of biological samples discrimination. The results illustrate the way to determine the set of depolarization metrics which optimizes tissue classification efficiencies. In that sense, the results show the interest of the method which is general, and which can be applied to study multiple types of biological samples, including of course human tissues. The latter can be useful for instance, to improve and to boost applications related to optical biopsy.

Eigenvectors of polarization coherency matrices

Calculation of the eigenvectors of two- and three-dimensional coherency matrices, and the four-dimensional coherency matrix associated with a Mueller matrix, is considered, especially for algebraic cases, in the light of recently published algorithms. The preferred approach is based on a combination of an evaluation of the characteristic polynomial and an adjugate matrix. The diagonal terms of the coherency matrix are given in terms of the characteristic polynomial of reduced matrices as functions of the eigenvalues of the coherency matrix. The analogous polynomial form for the off-diagonal elements of the coherency matrix is also presented. Simple expressions are given for the pure component in the characteristic decomposition.

Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rotations of the nD Cartesian reference frame and that are composed of two categories of meaningful parameters of different physical nature: the indices of population asymmetry and the intrinsic coherences. It is found that the components of purity coincide, up to respective simple coefficients, with the intrinsic Stokes parameters, which are also introduced in this work, and that determine two complementary sources of purity, namely the population asymmetry and the correlation asymmetry, whose weighted square average equals the overall degree of purity of ρ. A discriminating decomposition of ρ as a convex sum of three density matrices, viz. the pure, the fully random (maximally mixed) and the discriminating component, is introduced, which allows for the definition of the degree of nonregularity of ρ as the distance from ρ to a density matrix of a system composed of a pure component and a set of 2D, 3D,… and nD maximally mixed components. The chiral properties of a state ρ are analyzed and characterized from its intimate link to the degree of correlation asymmetry. The results presented constitute a generalization to nD systems of those established and exploited for polarization density matrices in a series of previous works.

Influence of temporal averaging in the performance of a rotating retarder imaging Stokes polarimeter

We study the optimum operating conditions for a rotating retarder fixed polarizer (RRFP) when the measurements are not quasi-instantaneous but time-averaged. We obtain the optimum retardance and retarder orientations as a function of the integrated angle interval. We also study how the increase in the number of time-averaged measurements leads to a better equally weighted variance (EWV) value, and thus, to a better performance of the polarimeter in terms of noise amplification for the case of additive noise. Two different analyzers configurations are studied in this work: uniformly spaced retarder angles and when measurements are taken at optimum angles (non-uniformly spaced angles). We also consider the case of polychromatic illumination. We discuss the best measurement conditions in terms of the signal-to-noise ratio depending on whether there is a fixed or a limited amount of photons per measurement.

The depolarization performances of scattering systems based on the Indices of Polarimetric Purity (IPPs)

In this paper, the Indices of Polarimetric Purity (IPPs) [1-3] have been proposed to analyze the depolarization performances of mono-dispersion and poly-dispersion scattering systems. Here, we mainly investigate the influences of the particles' density, Refractive Index (RI) of the medium, incident wavelengths, the mixing ratio of bi-dispersion scattering particles and particle-size distributions of poly-dispersion scattering system on the depolarization performances for the backscattering detection. For the mono-dispersion scattering system under same incident wavelength, if the relative RI ratios (m) increase linearly, the depolarization performances of the system will first weaken and then strengthen, and of course, the incident wavelength and density of scattering particles will also influence the depolarization performances of the scattering system. For the bi-dispersion scattering system, the proportion of small particles will be negatively correlated with the depolarization property of the dispersion system, and meanwhile, the particle-size distributions will also affect the depolarization performances greatly in the poly-dispersion scattering system. The results demonstrate that the IPPs can be used to describe the depolarization performances of dispersion systems effectively.

Eigenvalues of the coherency matrix for exact backscattering

An important approach to interpretation of the Mueller matrix is based on the eigenvalues of the coherency matrix, given by the roots of a quartic characteristic equation. For the case of backscattering, one eigenvalue is zero from reciprocity arguments, and the characteristic equation reduces to a cubic. These two approaches (quartic and cubic) to calculation of the eigenvalues for exact backscattering are analytically considered and compared. As expected, the cubic approach is usually simpler, but for the special case of two zero eigenvalues, either approach reduces to the predictions of the simple quadratic characteristic equation. Either approach can be used for numerical calculation of the eigenvalues. The variation in different purity measures with the values of the Mueller matrix elements is presented. An experimental Mueller matrix for backscattering from a turbid chiral medium is investigated.

Depolarizing metrics for plant samples imaging

Optical methods, as fluorescence microscopy or hyperspectral imaging, are commonly used for plants visualization and characterization. Another powerful collection of optical techniques is the so-called polarimetry, widely used to enhance image contrast in multiple applications. In the botanical applications framework, in spite of some works have already highlighted the depolarizing print that plant structures left on input polarized beams, the potential of polarimetric methods has not been properly exploited. In fact, among the few works dealing with polarization and plants, most of them study light scattered by plants using the Degree of Polarization (DoP) indicator. Other more powerful depolarization metrics are nowadays neglected. In this context, we highlight the potential of different depolarization metrics obtained using the Mueller matrix (MM) measurement: the Depolarization Index and the Indices of Polarimetric Purity. We perform a qualitative and quantitative comparison between DoP- and MM-based images by studying a particular plant, the Hedera maroccana. We show how Mueller-based metrics are generally more suitable in terms of contrast than DoP-based measurements. The potential of polarimetric measurements in the study of plants is highlighted in this work, suggesting they can be applied to the characterization of plants, plant taxonomy, water stress in plants, and other botanical studies.