Texture Analysis

Nuclear texture analysis is widely used in cancer research as a quantitative tool for the diagnosis and prognosis of human cancer.

Overview

Quantification of the chromatin structure in cell nuclei by texture analysis may improve the diagnostic and prognostic accuracy, and may also contribute towards a further understanding of the biological processes involved in carcinogenesis. In the texture analysis research project, we are developing and evaluating textural features with a potential diagnostic and prognostic value in tumour pathology. The aim is improved diagnostics and prognostics, leading to better and more focussed treatment of patients.

Research/Scientific

Nuclear texture analysis gives information about the spatial arrangement of the pixel gray levels in a digitized microscopic nuclear image and is a useful method to obtain quantitative information for the diagnosis and prognosis of human cancer. The chromatin structure, which both reflects and partially controls genetic functions, changes within cell nuclei as cancer develops. In convential pathology, atypical changes in cells and tissues are assessed subjectively during grading of malignancy and in diagnosis of patients. There is conciderable intra- and inter-pathologist variation in typing and grading of these visual changes. Therefore, quantification of both visual and sub-visual changes in cell nuclei may improve the diagnostic and prognostic accuracy, and may also contribute towards a further understanding of the biological processes involved in carcinogenesis.

In the development of a nuclear image analysis system, there are several different steps that need to be performed such as: preparing specimens, staining cells or tissues specifically for DNA, acquiring digital images of microscope fields, segmenting the cell nuclei from the digital images, extracting useful features from the segmented nuclei, evaluating and selecting features, designing a classifier based on training data, and testing the designed classifier on independent test data.

A large number of features have been proposed to describe the nuclei. The most commonly used features in nuclear image analysis are morphometric, densitometric and textural features. Morphometric features measure the size and shape of the nucleus and are independent of the gray level values of the pixels representing the nucleus. Densitometric features measure the overall optical density or gray level of the nucleus. Textural features provide measures of a number of properties such as contrast, smoothness, coarsness, randomness and structural complexity within the image.

In order to find nuclear features that discriminate between cases from different diagnostic and prognostic classes, a statistical evaluation of the features needs to be performed. In nuclear image analysis, it is common to evaluate a large number of features on a limited data set, without evaluating the results on an independent data set. This easily leads to over-optimistic results.

In a digital pathology situation where one seeks to classify samples based on texture analysis, the minimum complexity principle (Occamís Razor) is very relevant. According to this, the simplest model that explains the data is considered to be the best. So far, this principle has generally motivated the search for reduced feature sets in texture analysis and classification. A feature selection procedure may be applied in order to select a subset or a linear combination of the features available, either using a training data set to establish the set of features giving the smallest classification error, or using some functional feature space distance metric such that a large feature space distance implies a small classification error. However, the minimum complexity principle should also motivate us to generate only a few, but powerful, features. Identifying a few consistently valuable features is important as it improves classification reliability and enhances our understanding of the phenomena that we are modeling. The aim of the texture analysis research project is to develop and identify a few textural features that give reliable diagnostic and prognostic information, and to gain insight into which image chromatin structures that actually contains this type of information.

Technical

Within the field of texture analysis, a number of categories of methods exist, and even if we restrict ourselves to statistical methods, a large number of methods are available. Statistical approaches are considered to be generally applicable and work well for natural textures present in images. Statistical texture methods extract local information from the pixels of the image, and describe the distribution of this information in a statistical way. The extracted statistics may range from simple first-order statistics, such as mean value and standard deviation of the gray level distribution, to second-order or higher-order statistics, depending on the number of pixels which define the local information.

In many popular texture analysis methods, second order or higher order statistics on the relation between gray level values in pixel pairs or sequences of pixels are stored in matrices. Textural features are then extracted that directly describe the probability distribution within the matrix and, therefore, indirectly describe the image texture. Examples of such methods are the gray level cooccurrence matrix and the gray level run length matrix methods, which are commonly used in nuclear image analysis. The gray level cooccurrence matrix contains information on the relation between gray levels in pixel pairs, while the gray level run length matrix contains information on consecutive pixels with the same gray level, colinear in a given direction. A number of scalar texture features may be extracted from the cooccurrence or run length matrices. Many of these run length or cooccurrence features may be seen as a weighted sum of matrix element values, where the weighting applied to each element is based on a given weighting function. By varying this weighting function, different type of information about the texture can be extracted. The weighting functions fall into two general categories, i.e., weighting based on the value of the matrix element and weighting based on the position in the matrix.

The gray level entropy matrix method

As a part of the texture research project, we have developed a new texture method based on local gray level entropy. The entropy measures the non-uniformity or degree of scatter of pixel values within a window of size w x w pixels. Homogeneous structures will give low entropy values whereas inhomogeneous structures will give high entropy values.

The gray level entropy matrix element P(i,j) contains the estimated probability of an entropy value j within a window of a given size w centered around a pixel with gray level value i. The gray level entropy matrix is a parametric matrix, where the parameters are the window size w and the number of gray level quantization levels G in the image. By varying the values of the parameters w and G, several entropy matrices may be computed.

We have defined nine textural features based on local entropy values, i.e., scalar features which may be extracted from the gray level entropy matrices. Each feature is based on a weighted sum of the entropy matrix elements. The entropy features give an estimate of the gray-level disorder in different sizes of pixel neighborhoods. In a previous study, we have used the entropy-based textural features as a new prognostic tool in metastatic prostate cancer.

A partition of cell nuclei into periphery and center

In order to analyze the chromatin structure close to the nuclear membrane, we have used a spiral scanning algorithm which we call peel-off scanning. This is a straightforward venue to extract separate estimates of textural features in the periphery and center of nuclei. In several studies we have observed a radial differentiation of texture features within the nuclei.

Fractal dimension and lacunarity

The fractal dimension of a texture is a measure of complexity. Different fractal structures may share the same fractal dimension but have different appearance or textures. Therefore, fractal dimension alone may be of limited value in texture classification. Lacunarity may be seen as a measure of how fine or coarse a random fractal is. In the texture project we have proposed several new metods for estimating fractal parameters, i.e., fractal dimension and lacuarity, from images of cell nuclei. We have found that lacunarity is a powerful tool for analysis and classification of textures.

Adaptive low dimensional feature vectors

As described above, many statistical texture methods generate information about the statistics of the texture in the form of matrices. A number of pre-defined, non-adaptive features are then extracted from each probability matrix. This feature extraction may be repeated for several settings of some free parameters (e.g., number of gray levels in the image, inter-pixel distance, window size), resulting in a relatively high dimensionality of the feature space. Through several studies we have proposed a unified approach to extract only two adaptive features from each texture probability matrix. The adaptive feature extraction, which is based on a Mahalanobis class distance matrix and a class difference matrix, extracts texture features from the parts of the matrices which actually contain class distance information. In a comparative study, we found that the adaptive features outperformed the classical pre-defined features when applied to the most difficult set of 45 Brodatz texture pairs (which are often used for evaluation and comparison of texture methods). In several studies we have found that class distance and class difference matrices clearly illustrate the difference in texture between cell nucleus images from different prognostic (or diagnostic) classes. For each of the texture methods, one adaptive feature contains most of the discriminatory power of the method.

Nuclear area, DNA content and texture

The first-order gray level statistics of an image are affected by the image input conditions. Therefore, in texture analysis, the images are usually standardized to have the same mean value and standard deviation. However, in monolayer nuclei, there is a clear relation between nuclear integrated optical density (IOD), nuclear area, nuclear first-order gray level statistics and texture. Even diploid nuclei vary greately in first-order statistics and texture. In a previous study, we have found that it is important to consider this complex relation in nuclear texture analysis.

Mapping optimal texture features back onto images

It is important to advance our understanding of the interaction between structural and functional changes within the nuclei. As a part of the texture project, we will map the relative diagnostic or prognostic importance of textural features back onto the relevant parts of the images.