The idea of using a single-pixel photodetector to sense the world may sound a little bit ambitious. However, a new type of computational imaging technology termed computational ghost imaging (CGI), is indeed making it a reality. No longer satisfied with using a non-spatially resolved photodetector to ”see” the target, the computationally convolutional ghost imaging (CCGI) proposed in this paper can directly ”see” the target's features of interest without imaging first anymore. Rather than a conventional 4-f optical system, the CCGI scheme completes the convolution operations by optical methods with a single-pixel photodetector and an engineered structured illumination. Meanwhile, our CCGI scheme can adaptively work under sub-Nyquist sampling conditions, and it can facilitate real-time non-imaging edge detection of the real scene. With some multiplexing schemes, the prototype of CCGI has the potential as a new type of single-pixel computer vision that might be used as an optical frontend of a lightweight convolutional neural network to recognize objects intelligently. Our scheme brings new insights into both the convolution operation and the CGI technology, greatly broadening the application scenarios of CGI.