Method for optimizing channelized quadratic observers for binary classification of large-dimensional image datasets

Kupinski, Meredith; Clarkson, Eric

doi:10.1364/josaa.32.000549

Cited by 7 publications

(5 citation statements)

References 43 publications

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“…2 In this case, an optimal channel matrix can be constructed by using L eigenvectors of K −1 2 K 1 for the channels, with corresponding eigenvalues κ l . We showed in 2 that for J, the Bhattacharyya distance, and the AUC the eigenvectors are chosen to have the L largest values of κ l + κ −1 l .…”

Section: Methodsmentioning

confidence: 99%

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

et al. 2016

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To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first-and second-order statistics of the image data from both classes. The linear data reduction by the channels is described by an L × M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L × L instead of M × M , the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied. MOTIVATIONOur work is motivated by the need to develop a detection methodology to sort image data between two classes of objects (e.g. defect present and defect absent). To introduce the detection method begin by considering the relationship between an image and an object as g = Hf + n. Here g is an M × 1 vector of measurements made by an imaging system that is represented as a continuous-to-discrete operator H. The measurements of the continuous object f are corrupted by measurement noise n. We will consider post-processing signal detection. That is to say the forward imaging model H is fixed and can even be unknown since only the statistics of the image data g will be used. We are interested in linear combinations of the image data of the form v = Tg where T is an L × M channel matrix and compression is achieved since L < M . Using terminology from the perception literature, each row of T is referred to as a channel and v is the channelized data. 1 Given a fixed set of L channels the optimal classifier will compute the channelized log-likelihoodand compare this decision variable λ to a threshold to sort the image data into one of two classes. For notational purposes the classes are denoted by i = 1, 2. In this work we assume the channelized likelihoods pr i (Tg) are Gaussian. Since the channelized data are weighted sums of the image data they may be at least approximately Gaussian distributed, as long as the image data are sufficiently independent, even if the original data are not. In this case we would ...

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Section: Methodsmentioning

confidence: 99%

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

et al. 2016

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“…The Bhattacharyya distance has also been used to optimize a single PSG/PSA measurement without a closed-form gradient [5]. The mathematical and empirical relationship between J and AUC is described in [23].…”

Section: Psg/psa Optimizationmentioning

confidence: 99%

Evaluating the Utility of Mueller Matrix Imaging for Diffuse Material Classification

Kupinski¹,

Li²

2020

jist

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Evaluating the utility of polarimetric imaging for material identification, as compared to conventional irradiance imaging, motivates this work. Images of diffuse objects captured with a wide field of view Mueller matrix polarimeter are used to demonstrate a classification and measurement optimization method. This imaging study is designed to test polarimetric utility in discriminating white fabric from white wood. The material color is constrained to be similar so that classification from only total radiance imaging is difficult, i.e., metamerism. A statistical divergence between two distributions of measured intensity is used to optimize the Polarization State Generator (PSG) and the Polarization State Analyzer (PSA) given two classes of Mueller matrices. The classification performance as a function of number of polarimetric measurements is computed. This work demonstrates that two polarimetric measurements of white fabric and white wood offer nearly perfect classification. The utility and design of partial Mueller imaging is supported by this optimization of PSG/PSA states and number of measurements.

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“…Fukunaga and Koontz were the first to suggest covariance matrix eigendecomposition for detection and classification tasks [14]. With certain eigenspectrum assumptions, the Fukunaga-Koontz transform (FKT) is the low-rank approximation to the optimal classifier for zero mean, heteroscadastic, and normally distributed data [15,16]. An adaptation of FKT widely used in pattern recognition, is called a tuned basis function (TBF) [17].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

“…The FKT matrix is populated by L eigenvectors of K −1 2 K 1 with corresponding eigenvalues κ l . The IO AUC can be maximized when these eigenvectors are chosen to have the L largest values of κ l + κ −1 l [16]. Then the compressed data is t = T g,…”

Section: Channelized Images: Linear Data Transformationmentioning

confidence: 99%

Limitations of CNNs for Approximating the Ideal Observer Despite Quantity of Training Data or Depth of Network

Omer¹,

Caucci²,

Kupinski³

2020

jist

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The performance of a convolutional neural network (CNN) on an image texture detection task as a function of linear image processing and the number of training images is investigated. Performance is quantified by the area under (AUC) the receiver operating characteristic (ROC) curve. The Ideal Observer (IO) maximizes AUC but depends on high-dimensional image likelihoods. In many cases, the CNN performance can approximate the IO performance. This work demonstrates counterexamples where a full-rank linear transform degrades the CNN performance below the IO in the limit of large quantities of training data and network layers. A subsequent linear transform changes the images’ correlation structure, improves the AUC, and again demonstrates the CNN dependence on linear processing. Compression strictly decreases or maintains the IO detection performance while compression can increase the CNN performance especially for small quantities of training data. Results indicate an optimal compression ratio for the CNN based on task difficulty, compression method, and number of training images.

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Method for optimizing channelized quadratic observers for binary classification of large-dimensional image datasets

Cited by 7 publications

References 43 publications

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

Evaluating the Utility of Mueller Matrix Imaging for Diffuse Material Classification

Limitations of CNNs for Approximating the Ideal Observer Despite Quantity of Training Data or Depth of Network

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