# Fuzzy Windows with Gaussian Processed Labels for Ordinal Image Scoring Tasks
## 1 Introduction  
Image scoring, typically known as ordinal classification, is a supervised learning problem aiming to predict a discrete set of ordinal labels. The main difference from the classification task is that the categories are related in a natural or implied order. For example, the apparent age group estimation grades face images based on an ordinal scale: \"infants\", \"children\", \"teenagers\", \"youth\", \"young adults\", \"adults\", \"middle-aged\", and \"aged\". Ordinal classification can be viewed as a special case of metric regression, where the regression targets are discrete and finite. The differences in features between adjacent labels are not always equal to each other. The difference in facial features between \"infants\" and \"children\" being more obvious than facial features between \"young adults\" and \"adults\" is one example. However, if the ordinal relationship of labels is ignored, the ordinal regression problem will only become a simple multi-class classification issue. In Figure 1, when learning with ordinal images, a common problem is that the ambiguity between two neighboring categories usually has a negative effect on the training convergence. Therefore, the performance of the learned model tends to degrade in ordinal classes. This challenge has motivated us to develop a robust ordinal image classification approach to analyzing ordinal data. Ordinal image classification approaches or ordinal models [1] can be roughly divided into two aspects, Single Label Learning with Specific Loss (SLL-Loss) [2; 3; 4; 5] and the Label Distribution Based Learning (LDBL) [2; 6; 7; 8; 9; 10; 11; 12; 13]. SLL-Loss methods typically rely on independently processing a single facial image. This ignores gradual changes in human faces, andthus, facial appearance is usually ambiguous as regards adjacent age classes. The LDBL methods tend to map ordinal ground-truth learning based on a Gaussian or Gaussian-like label distribution. But under such a long-tailed case, they also ignore the processing of ordinal neighbors or overlapping features. To address the ambiguous and overlapping features in the ordinal data, we propose a Fuzzy Window with the Gaussian Processed Labels (FW-GPL) approach to the ordinal classification issue. This also aims to stretch the semantic margins (or enlarge their interclass variance) of ordinal classes, which represent the shared features of neighbor categories. As shown in Figure 1, we assume that two neighboring ordinal classes have a closely shared feature region which can increase the difficulty of the ordinal classification task. A fuzzy window with Gaussian processed labels is carefully designed on the top of deep neural networks so as to reduce the effect of the overlapping features but preserve the age distribution information. In Figure 2, our proposed FW-GPL is composed of two crucial branches, including a defuzzifier window and a learning strategy using Gaussian processed labels. The defuzzifier window attempts to reduce the influence the ambiguously overlapping features have on ordinal neighbors, and simultaneously, it tries to retain the internal ordinal features which can represent the real category. Practically, the Gaussian processed labels allow the incorporation of prior knowledge (e.g., Gaussian-like age distribution) to concentrate on the major class and weaken the influence of remote neighbor classes. To validate the effectiveness of our proposed method, we perform extensive experiments on three widely-used face-aging datasets, including MORPH II [14], FG-NET [15], and CACD [16], as well as one medical ordinal dataset: Curated Breast Imaging Subset of Digital Database of Screening Mammography (CBIS-DDSM). This paper proposes a novel Fuzzy Window with a Gaussian Processed Label (FW-GPL) method for ordinal image scoring, and we achieve a competitive performance compared to State-Of-The-Art (SOTA) methods. The main contributions of this work are summarized as follows:  
Figure 1: The challenge of ordinal image classification (or scoring).