This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of the moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. This property makes Tchebichef moments superior to the conventional orthogonal moments such as Legendre moments and Zernike moments, in terms of preserving the analytical properties needed to ensure information redundancy in a moment set. The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.

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Abstract-Discrete orthogonal moments have several computational advantages over continuous moments. However, when the moment order becomes large, discrete orthogonal moments (such as the Tchebichef moments) tend to exhibit numerical instabilities. This paper introduces the orthonormal version of Tchebichef moments, and analyzes some of their computational aspects. The recursive procedure used for polynomial evaluation can be suitably modified to reduce the accumulation of numerical errors. The proposed set of moments can be used for representing image shape features and for reconstructing an image from its moments with a high degree of accuracy.

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Aims: Evaluating expression of the human epidermal growth factor receptor 2 (HER2) by visual examination of immunohistochemistry (IHC) on invasive breast cancer (BCa) is a key part of the diagnostic assessment of BCa due to its recognized importance as a predictive and prognostic marker in clinical practice. However, visual scoring of HER2 is subjective, and consequently prone to interobserver variability. Given the prognostic and therapeutic implications of HER2 scoring, a more objective method is required. In this paper, we report on a recent automated HER2 scoring contest, held in conjunction with the annual PathSoc meeting held in Nottingham in June 2016, aimed at systematically comparing and advancing the state-of-the-art artificial intelligence (AI)-based automated methods for HER2 scoring. Methods and results: The contest data set comprised digitized whole slide images (WSI) of sections from 86 cases of invasive breast carcinoma stained with both haematoxylin and eosin (H&E) and IHC for HER2. The contesting algorithms predicted scores of the IHC slides automatically for an unseen subset of the data set and the predicted scores were compared with the 'ground truth' (a consensus score from at least two experts). We also report on a simple 'Man versus Machine' contest for the scoring of HER2 and show Address for correspondence: N Rajpoot and T Qaiser, Department of Computer Science, University of Warwick, UK. e-mails: n.m.rajpoot@ warwick.ac.uk; t.qaiser@warwick.ac.uk *These authors contributed equally to this study. 2018 , 72, 227-238. DOI: 10.1111 that the automated methods could beat the pathology experts on this contest data set. Conclusions: This paper presents a benchmark for comparing the performance of automated algorithms for scoring of HER2. It also demonstrates the enormous potential of automated algorithms in assisting the pathologist with objective IHC scoring.

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