Abstract: Recently, the field of Image Coding for Machines (ICM) has garnered heightened interest and significant advances thanks to the rapid progress of learning-based techniques for image compression and analysis. Previous studies often require training separate codecs to support various bitrate levels, machine tasks, and networks, thus lacking both flexibility and practicality. To address these challenges, we propose a rate-distortion-cognition controllable versatile image compression, which method allows the users to adjust the bitrate (i.e., Rate), image reconstruction quality (i.e., Distortion), and machine task accuracy (i.e., Cognition) with a single neural model, achieving ultra-controllability. Specifically, we first introduce a cognition-oriented loss in the primary compression branch to train a codec for diverse machine tasks. This branch attains variable bitrate by regulating quantization degree through the latent code channels. To further enhance the quality of the reconstructed images, we employ an auxiliary branch to supplement residual information with a scalable bitstream. Ultimately, two branches use a `$\beta x + (1 - \beta) y$' interpolation strategy to achieve a balanced cognition-distortion trade-off. Extensive experiments demonstrate that our method yields satisfactory ICM performance and flexible Rate-Distortion-Cognition controlling.