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Histopathological Image Classification using Discriminative Feature-oriented Dictionary Learning

Tiep Huu Vu, Hojjat Seyed Mousavi, Vishal Monga, Arvind UK Rao, Ganesh Rao

arXiv:1506.05032v5cs.CV

TL;DR

Histopathological classification requires reliable discriminative features despite diverse tissue structures and geometrical richness. DFDL learns sparse, class-specific dictionaries for low-complexity classification and disease grading, and experiments across three datasets show competitive or superior performance, especially with limited training data.

  • Problem

    Histopathological image classification needs reliable discriminative features because tissue images contain diverse histology features and rich geometrical structures.

  • Method

    DFDL learns discriminative class-specific dictionaries that sparsely represent in-class samples while limiting representation of samples from other classes.

  • Results

    Across three diverse histopathological datasets, DFDL is competitive with or outperforms state-of-the-art alternatives, including on disease detection and ROC performance.

  • Takeaways & Limitations

    DFDL is presented as a broadly applicable candidate for automated histopathological diagnosis, requiring minimal parameter tuning and lower complexity than competing methods.

Abstract

from arXiv · show

In histopathological image analysis, feature extraction for classification is a challenging task due to the diversity of histology features suitable for each problem as well as presence of rich geometrical structures. In this paper, we propose an automatic feature discovery framework via learning class-specific dictionaries and present a low-complexity method for classification and disease grading in histopathology. Essentially, our Discriminative Feature-oriented Dictionary Learning (DFDL) method learns class-specific dictionaries such that under a sparsity constraint, the learned dictionaries allow representing a new image sample parsimoniously via the dictionary corresponding to the class identity of the sample. At the same time, the dictionary is designed to be poorly capable of representing samples from other classes. Experiments on three challenging real-world image databases: 1) histopathological images of intraductal breast lesions, 2) mammalian kidney, lung and spleen images provided by the Animal Diagnostics Lab (ADL) at Pennsylvania State University, and 3) brain tumor images from The Cancer Genome Atlas (TCGA) database, reveal the merits of our proposal over state-of-the-art alternatives. {Moreover, we demonstrate that DFDL exhibits a more graceful decay in classification accuracy against the number of training images which is highly desirable in practice where generous training is often not available

I. INTRODUCTION

Histopathological classification is difficult because tissue images contain rich, problem-specific geometric and morphological features. The paper introduces DFDL to discover discriminative features through class-specific dictionaries and evaluates it across diverse diagnostic tasks.

  • Histopathological images require customized features because tissues from different organs exhibit diverse structural and morphological patterns.
  • DFDL learns class-specific dictionaries that represent in-class samples with few bases while keeping complementary samples far from the corresponding sparse subspaces.
  • Experiments use three diverse histopathological datasets to assess broad applicability across distinct classification and detection problems.
  • The method targets automatic feature discovery and classification for breast lesions, brain-tumor MVP detection, and healthy-versus-inflammatory mammalian-organ images.
  • The paper reports complexity analysis, reproducible software, and performance comparisons with existing dictionary-learning methods.

II. CONTRIBUTIONS

DFDL formulates class-specific dictionary learning as a sparsity-constrained optimization problem. Its design favors sparse representation of in-class samples and poor representation of complementary samples, followed by residual-based classification.

  • A. Notation: Each image patch is vectorized as a sample y, while Yi contains class-i samples, complementary samples are stored in Ȳi, and Di denotes the class-i dictionary.
  • B. Discriminative Feature-oriented Dictionary Learning: The learned dictionary should sparsely represent class-i samples while representing complementary samples poorly with a small number of bases.
  • B. Discriminative Feature-oriented Dictionary Learning: DFDL minimizes intra-class differences and emphasizes inter-class differences through a regularized optimization problem for each class.
  • B. Discriminative Feature-oriented Dictionary Learning: The sparsity level L must balance adequate in-class representation against preventing representation of complementary samples.
  • B. Discriminative Feature-oriented Dictionary Learning: An ODL initialization estimates sparsity, while classification codes a new patch over the concatenated dictionaries and assigns the class with the smallest class-specific residual.

C. Proposed solution

DFDL alternates sparse-code optimization with dictionary updates, using a convexification step to handle the dictionary-update objective when it is not guaranteed to be convex.

  • Optimization procedure: DFDL alternates between fixing the dictionary while optimizing sparse codes and fixing the codes while updating the dictionary.The algorithm repeats these stages until convergence.
  • Sparse coding: The sparse coding problems are combined using all in-class and complementary training samples and solved effectively with OMP.The implementation uses the SPAMS toolbox.
  • Convexification: The dictionary-update objective is not guaranteed to be convex because the associated symmetric matrix F may not be positive semidefinite.In the worst case, applying the usual update algorithm would produce a maximum rather than a minimum.
  • Convexification: The method convexifies dictionary updating by subtracting a constant based on the minimum eigenvalue of F after constraining dictionary-column norms.The shifted matrix F̂ is positive semidefinite, making the resulting objective convex.

D. Overall classification procedures for three datasets

The paper applies a DFDL-based classification procedure to three histopathological image datasets.

  • A DFDL-based procedure is proposed for classifying images in three datasets.

1) IBL and ADL datasets

For IBL and ADL images, DFDL learns class-specific dictionaries from labeled patches and classifies new images through patch-level decisions aggregated into an image-level feature.

  • Training: Training patches are randomly extracted from labeled healthy and diseased images, with patch size selected using pathologist input or cross-validation.Class-specific DFDL dictionaries are then learned from the healthy and diseased patch sets.
  • Patch classification: Each test image is divided into non-overlapping patches, and every patch is classified with the DFDL classifier.
  • Image classification: The proportion of healthy patches becomes a one-dimensional image feature that is supplied to a simple SVM.A threshold θ is selected so healthy and diseased images fall on opposite sides of the specified healthy-patch proportions.

2) MVP detection problem in TCGA dataset

MVP detection addresses brain-tumor regions that are difficult to identify because a single MVP region can indicate a high-grade tumor and requires larger-scale investigation than IBL or ADL classification.

  • Problem setting: MVP is an important indicator of high-grade brain glioma, and one MVP region can indicate a high-grade tumor.
  • Patch and region labels: The TCGA procedure labels patches as MVP only when they lie entirely within an MVP region; otherwise they are labeled Not MVP.A region is Not MVP when it contains no MVP patch.
  • Training phase: DFDL dictionaries are learned from manually extracted MVP and Not MVP regions, with Not MVP regions potentially drawn from all images.
  • Comparisons: The experiments compare DFDL with WND-CHARM plus SVM, SRC, SHIRC, LC-KSVD, FDDL, and Nayak’s sparse feature-learning method.LC-KSVD and FDDL use dictionaries learned from the same training patches for a fair comparison.

A. Experimental Set-Up: Image Datasets

DFDL was evaluated on diverse histopathological datasets using learned bases, sparse codes, and classification-accuracy comparisons against competing methods. The experiments covered breast lesions, bovine kidney, lung, spleen, and TCGA brain-tumor images.

  • Datasets: The IBL dataset used 120 regions of interest, with 20 images for training and 100 for testing after downsampling.Experiments used 10 training images per class and 20-by-20 patches.
  • Datasets: The ADL dataset contained healthy and inflammatory bovine images from kidney, lung, and spleen sub-datasets.Each sub-dataset had roughly 150 images per class, with 40 images selected for training and the remainder for testing.
  • Datasets: The TCGA dataset contained 190 regions of interest, including 57 with MVP regions and 133 without, with 20 training images selected from each class.The images had 3000×3000 resolution.
  • Validation design: DFDL experiments tested whether sparsity-driven class-specific bases emphasize inter-class differences while keeping intra-class differences small.The evaluation examined whether the resulting bases were discriminative for classification.
  • Feature visualization: Visualized DFDL bases captured disease-relevant morphology, including cell distributions in spleen, cell shapes in IBL, and alveolar structure in lung images.In lung images, normal bases showed more white regions, whereas inflammatory bases reflected inflammatory-cell-filled alveoli.
  • Classification accuracy: DFDL achieved over 97.75% accuracy on IBL and ADL-Lung, nearly 90% on ADL-Kidney, and over 92% on ADL-Spleen.The IBL and ADL-Lung results exceeded the next-best reported rates of 92.85% and 91.56%, respectively.

D. Complexity analysis

The experiments compare DFDL with competing methods across classification accuracy, ROC behavior, and dependence on training data. DFDL is reported as computationally efficient, strong in disease detection, and comparatively robust when training resources or dictionary bases are reduced.

  • Complexity comparison: DFDL is reported as the least expensive computational method among the compared dictionary-learning approaches.The comparison includes LC-KSVD, FDDL, and Nayak’s method.
  • Confusion matrices: DFDL offers the best disease detection accuracy in almost all datasets for each organ while maintaining high healthy-image classification accuracy.
  • ROC analysis: DFDL’s ROC curves perform best compared with other state-of-the-art methods across the three datasets.The ROC operating point balances miss and false-alarm probabilities.
  • Training-set dependence: DFDL exhibits the most graceful decline in overall classification accuracy as the training set is reduced.The comparison covers IBL and ADL datasets and varies training patches and images.
  • Training-set dependence: WND-CHARM has no result in the training-patch comparison because it operates at the whole-image level.

G. Performance vs. number of training bases

When the number of dictionary bases varies from 200 to 600, DFDL continues to outperform competing methods and maintains high accuracy as the number of bases decreases. These results are presented as evidence of parameter robustness and practical applicability across histopathology problems.

  • Performance versus training bases: DFDL outperforms other methods as the number of dictionary bases varies from 200 to 600.Patch size is fixed at 20 × 20 pixels in this comparison.
  • Performance versus training bases: DFDL maintains high overall accuracy on different datasets when the number of training bases is reduced.
  • Performance versus training bases: The results illustrate that DFDL is fairly robust to parameter changes.The paper identifies this robustness as desirable in practice.
  • Practical applicability: The method is reported to be competitive with or better than state-of-the-art alternatives, particularly with realistic or limited training-set sizes.

APPENDIX

The appendix analyzes computational complexity by focusing on sparse coding, which dominates dictionary updates in most dictionary-learning methods. It derives the approximate operation count for DFDL and frames corresponding comparisons with LC-KSVD.

  • Complexity analysis: Sparse coding dominates dictionary-update complexity in most dictionary-learning methods.The analysis focuses on sparse-coding complexity in each iteration.
  • DFDL complexity: DFDL’s most expensive computation is solving an Orthogonal Matching Pursuit problem.The problem is defined for samples Y, dictionary D, and sparsity level L.
  • DFDL complexity: Under L ≪ k ≈ d ≪ N, the Batch-OMP complexity expression can be simplified asymptotically.The appendix cites the Batch-OMP complexity reported by Rubinstein et al.
  • DFDL complexity: DFDL solves c sparse-coding problems, yielding total complexity T_DFDL ≈ c^2kN(2d + L^2).
  • LC-KSVD complexity: The appendix compares LC-KSVD1 using a K-SVD-form optimization and reports T_LC-KSVD ≈ c^2kN(2d + 2ck + L^2).LC-KSVD2 is excluded because it has higher complexity.

C. Complexity of Nayak’s

The appendix characterizes Nayak’s sparse-coding cost through iterative gradient descent. Its complexity accounts for matrix multiplications and the average number of iterations required for convergence.

  • Sparse coding: Nayak’s method estimates S using gradient descent, with each iteration computing the gradient of Q(S) = ∥Y−DS∥2_F.
  • Sparse coding: The complexity analysis precomputes D⊤D + I and (D⊤−W)Y, while recalculating (D⊤D + I)S after updates to S.
  • Complexity assumptions: The estimated cost includes q, the average number of iterations needed for convergence.The analysis ignores matrix additions, subtractions, and scalar multiplications.

D. Complexity of FDDL

The FDDL sparse-coding complexity is derived by accounting for precomputation and iterative gradient costs, then extending the class-specific cost across c classes. The resulting total cost is approximately expressed by TFDDL.

  • Gradient computation: The optimization uses Iterative Projective Method, whose per-iteration complexity depends on gradients of six Frobenius-norm terms.The first three terms use precomputed D⊤D and D⊤Y_i products; the remaining terms are handled separately.
  • Gradient computation: The computational cost of evaluating (19) with q iterations is cdk(2N + ck) + 2qc^2k^2N.The expression combines precomputation with repeated costs for computing (D⊤D)S_i.
  • Algebraic simplification: The remaining terms can be simplified using an all-one matrix E_m,n, enabling lower-cost calculations for equations (21), (22), and (23).The text states that E_m,n is an all-one matrix in R^m×n and uses simple algebra for the subsequent derivations.
  • Overall complexity: Compared with (19), equations (21)–(23) require much less computation, so the total cost of solving S_i is approximately the cost in (20).The sparse-coding cost for FDDL is then estimated by multiplying the class-specific problem cost by c.
  • Overall complexity: TFDDL ≈ c^2dk(2N + ck) + 2qc^3k^2N = c^2kN(2d + 2qck) + c^3dk^2.This is the reported approximate total cost for the sparse-coding step of FDDL.
  • Comparison: Final analyzed results for four different dictionary-learning methods are reported in Table II.
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