Fast and exact computation of moments using discrete Green's theorem

Green's theorem evaluates a double integral over the region of an object by a simple integration along the boundary of the object. It has been used in moment computation since the shape of a binary object is totally determined by its boundary. By using a discrete analogue of Green's theorem, we present a new algorithm for fast computation of geometric moments. The algorithm is faster than previous methods, and gives exact results. The importance of exact computation is discussed by examining the invariance of Hu's moments. A fast method for computing moments of regions in grey level image, using discrete Green's theorem, is also presented

The Use of Fractal Features from the Periphery of Cell Nuclei as a Classification Tool

A polygonization‐based method is used to estimate the fractal dimension and several new scalar lacunarity features from digitized transmission electron micrographs (TEM) of mouse liver cell nuclei. The fractal features have been estimated in different segments of 1D curves obtained by scanning the 2D cell nuclei in a spiral‐like fashion called “peel‐off scanning”. This is a venue to separate estimates of fractal features in the center and periphery of a cell nucleus. Our aim was to see if a small set of fractal features could discriminate between samples from normal liver, hyperplastic nodules and hepatocellular carcinomas. The Bhattacharyya distance was used to evaluate the features. Bayesian classification with pooled covariance matrix and equal prior probabilities was used as the rule for classification. Several single fractal features estimated from the periphery of the cell nuclei discriminated samples from the hyperplastic nodules and hepatocellular carcinomas from normal ones. The outer 25–30% of the cell nuclei contained important texture information about the differences between the classes. The polygonization‐based method was also used as an analysis tool to relate the differences between the classes to differences in the chromatin structure

A Review of Caveats in Statistical Nuclear Image Analysis

A large body of the published literature in nuclear image analysis do not evaluate their findings on an independent data set. Hence, if several features are evaluated on a limited data set over‐optimistic results are easily achieved. In order to find features that separate different outcome classes of interest, statistical evaluation of the nuclear features must be performed. Furthermore, to classify an unknown sample using image analysis, a classification rule must be designed and evaluated. Unfortunately, statistical evaluation methods used in the literature of nuclear image analysis are often inappropriate. The present article discusses some of the difficulties in statistical evaluation of nuclear image analysis, and a study of cervical cancer is presented in order to illustrate the problems. In conclusion, some of the most severe errors in nuclear image analysis occur in analysis of a large feature set, including few patients, without confirming the results on an independent data set. To select features, Bonferroni correction for multiple test is recommended, together with a standard feature set selection method. Furthermore, we consider that the minimum requirement of performing statistical evaluation in nuclear image analysis is confirmation of the results on an independent data set. We suggest that a consensus of how to perform evaluation of diagnostic and prognostic features is necessary, in order to develop reliable tools for clinical use, based on nuclear image analysis

Association Between Proportion of Nuclei With High Chromatin Entropy and Prognosis in Gynecological Cancers

Background: Nuclear texture analysis measuring differences in chromatin structure has provided prognostic biomarkers in several cancers. There is a need for improved cell-by-cell chromatin analysis to detect nuclei with highly disorganized chromatin. The purpose of this study was to develop a method for detecting nuclei with high chromatin entropy and to evaluate the association between the presence of such deviating nuclei and prognosis. Methods: A new texture-based biomarker that characterizes each cancer based on the proportion of high–chromatin entropy nuclei (<25% vs ≥25%) was developed on a discovery set of 175 uterine sarcomas. The prognostic impact of this biomarker was evaluated on a validation set of 179 uterine sarcomas, as well as on independent validation sets of 246 early-stage ovarian carcinomas and 791 endometrial carcinomas. More than 1 million images of nuclei stained for DNA were included in the study. All statistical tests were two-sided. Results: An increased proportion of high–chromatin entropy nuclei was associated with poor clinical outcome. The biomarker predicted five-year overall survival for uterine sarcoma patients with a hazard ratio (HR) of 2.02 (95% confidence interval [CI] = 1.43 to 2.84), time to recurrence for ovarian cancer patients (HR = 2.91, 95% CI = 1.74 to 4.88), and cancer-specific survival for endometrial cancer patients (HR = 3.74, 95% CI = 2.24 to 6.24). Chromatin entropy was an independent prognostic marker in multivariable analyses with clinicopathological parameters (HR = 1.81, 95% CI = 1.21 to 2.70, for sarcoma; HR = 1.71, 95% CI = 1.01 to 2.90, for ovarian cancer; and HR = 2.03, 95% CI = 1.19 to 3.45, for endometrial cancer). Conclusions: A novel method detected high–chromatin entropy nuclei, and an increased proportion of such nuclei was associated with poor prognosis. Chromatin entropy supplemented existing prognostic markers in multivariable analyses of three gynecological cancer cohorts.publishedVersio

Deep learning for prediction of colorectal cancer outcome: a discovery and validation study

Background Improved markers of prognosis are needed to stratify patients with early-stage colorectal cancer to refine selection of adjuvant therapy. The aim of the present study was to develop a biomarker of patient outcome after primary colorectal cancer resection by directly analysing scanned conventional haematoxylin and eosin stained sections using deep learning. Methods More than 12 000 000 image tiles from patients with a distinctly good or poor disease outcome from four cohorts were used to train a total of ten convolutional neural networks, purpose-built for classifying supersized heterogeneous images. A prognostic biomarker integrating the ten networks was determined using patients with a non-distinct outcome. The marker was tested on 920 patients with slides prepared in the UK, and then independently validated according to a predefined protocol in 1122 patients treated with single-agent capecitabine using slides prepared in Norway. All cohorts included only patients with resectable tumours, and a formalin-fixed, paraffin-embedded tumour tissue block available for analysis. The primary outcome was cancer-specific survival. Findings 828 patients from four cohorts had a distinct outcome and were used as a training cohort to obtain clear ground truth. 1645 patients had a non-distinct outcome and were used for tuning. The biomarker provided a hazard ratio for poor versus good prognosis of 3·84 (95% CI 2·72–5·43; p<0·0001) in the primary analysis of the validation cohort, and 3·04 (2·07–4·47; p<0·0001) after adjusting for established prognostic markers significant in univariable analyses of the same cohort, which were pN stage, pT stage, lymphatic invasion, and venous vascular invasion. Interpretation A clinically useful prognostic marker was developed using deep learning allied to digital scanning of conventional haematoxylin and eosin stained tumour tissue sections. The assay has been extensively evaluated in large, independent patient populations, correlates with and outperforms established molecular and morphological prognostic markers, and gives consistent results across tumour and nodal stage. The biomarker stratified stage II and III patients into sufficiently distinct prognostic groups that potentially could be used to guide selection of adjuvant treatment by avoiding therapy in very low risk groups and identifying patients who would benefit from more intensive treatment regimes

Chromatin organisation and cancer prognosis: a pan-cancer study

Background: Chromatin organisation affects gene expression and regional mutation frequencies and contributes to carcinogenesis. Aberrant organisation of DNA has been correlated with cancer prognosis in analyses of the chromatin component of tumour cell nuclei using image texture analysis. As yet, the methodology has not been sufficiently validated to permit its clinical application. We aimed to define and validate a novel prognostic biomarker for the automatic detection of heterogeneous chromatin organisation. Methods Machine learning algorithms analysed the chromatin organisation in 461 000 images of tumour cell nuclei stained for DNA from 390 patients (discovery cohort) treated for stage I or II colorectal cancer at the Aker University Hospital (Oslo, Norway). The resulting marker of chromatin heterogeneity, termed Nucleotyping, was subsequently independently validated in six patient cohorts: 442 patients with stage I or II colorectal cancer in the Gloucester Colorectal Cancer Study (UK); 391 patients with stage II colorectal cancer in the QUASAR 2 trial; 246 patients with stage I ovarian carcinoma; 354 patients with uterine sarcoma; 307 patients with prostate carcinoma; and 791 patients with endometrial carcinoma. The primary outcome was cancer-specific survival. Findings: In all patient cohorts, patients with chromatin heterogeneous tumours had worse cancer-specific survival than patients with chromatin homogeneous tumours (univariable analysis hazard ratio [HR] 1·7, 95% CI 1·2–2·5, in the discovery cohort; 1·8, 1·0–3·0, in the Gloucester validation cohort; 2·2, 1·1–4·5, in the QUASAR 2 validation cohort; 3·1, 1·9–5·0, in the ovarian carcinoma cohort; 2·5, 1·8–3·4, in the uterine sarcoma cohort; 2·3, 1·2–4·6, in the prostate carcinoma cohort; and 4·3, 2·8–6·8, in the endometrial carcinoma cohort). After adjusting for established prognostic patient characteristics in multivariable analyses, Nucleotyping was prognostic in all cohorts except for the prostate carcinoma cohort (HR 1·7, 95% CI 1·1–2·5, in the discovery cohort; 1·9, 1·1–3·2, in the Gloucester validation cohort; 2·6, 1·2–5·6, in the QUASAR 2 cohort; 1·8, 1·1–3·0, for ovarian carcinoma; 1·6, 1·0–2·4, for uterine sarcoma; 1·43, 0·68–2·99, for prostate carcinoma; and 1·9, 1·1–3·1, for endometrial carcinoma). Chromatin heterogeneity was a significant predictor of cancer-specific survival in microsatellite unstable (HR 2·9, 95% CI 1·0–8·4) and microsatellite stable (1·8, 1·2–2·7) stage II colorectal cancer, but microsatellite instability was not a significant predictor of outcome in chromatin homogeneous (1·3, 0·7–2·4) or chromatin heterogeneous (0·8, 0·3–2·0) stage II colorectal cancer. Interpretation: The consistent prognostic prediction of Nucleotyping in different biological and technical circumstances suggests that the marker of chromatin heterogeneity can be reliably assessed in routine clinical practice and could be used to objectively assist decision making in a range of clinical settings. An immediate application would be to identify high-risk patients with stage II colorectal cancer who might have greater absolute benefit from adjuvant chemotherapy. Clinical trials are warranted to evaluate the survival benefit and cost-effectiveness of using Nucleotyping to guide treatment decisions in multiple clinical settings