While object detection methods traditionally make use of pixel-level masks or bounding boxes, alternative representations such as polygons or active contours have recently emerged. Among them, methods based on the regression of Fourier or Chebyshev coefficients have shown high potential on freeform objects. By defining object shapes as polar functions, they are however limited to star-shaped domains. We address this issue with SCR, a method that captures resolution-free object contours as complex periodic functions. The method offers a good compromise between accuracy and compactness thanks to the design of efficient geometric shape priors. We benchmark SCR on the popular COCO 2017 instance segmentation dataset, and show its competitiveness against existing algorithms in the field. In addition, we design a compact version of our network, which we benchmark on embedded hardware with a wide range of power targets, achieving up to real-time performance.