Quantifying image complexity at the entity level is straightforward, but the assessment of semantic complexity has been largely overlooked. In fact, there are differences in semantic complexity across images. Images with richer semantics can tell vivid and engaging stories and offer a wide range of application scenarios. For example, the Cookie Theft picture is such a kind of image and is widely used to assess human language and cognitive abilities due to its higher semantic complexity. Additionally, semantically rich images can benefit the development of vision models, as images with limited semantics are becoming less challenging for them. However, such images are scarce, highlighting the need for a greater number of them. For instance, there is a need for more images like Cookie Theft to cater to people from different cultural backgrounds and eras. Assessing semantic complexity requires human experts and empirical evidence. Automatic evaluation of how semantically rich an image will be the first step of mining or generating more images with rich semantics, and benefit human cognitive assessment, Artificial Intelligence, and various other applications. In response, we propose the Image Semantic Assessment (ISA) task to address this problem. We introduce the first ISA dataset and a novel method that leverages language to solve this vision problem. Experiments on our dataset demonstrate the effectiveness of our approach. Our data and code are available at: https://github.com/xiujiesong/ISA.

We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high dimensional' ISA problem can be handled by a recent technique called joint f-decorrelation (JFD). Similar decorrelation methods have been used previously for kernel independent component analysis (kernel-ICA). More precisely, the kernel canonical correlation (KCCA) technique is a member of this family, and, as is shown in this paper, the kernel generalized variance (KGV) method can also be seen as a decorrelation method in the feature space. These kernel based algorithms will be adapted to the ISA task. In the numerical examples, we (i) examine how efficiently the emerging higher dimensional ISA tasks can be tackled, and (ii) explore the working and advantages of the derived kernel-ISA methods.