Several recent studies have used radial frequency patterns to investigate intermediate-level shape perception, a critical precursor to object recognition. Here, we developed the first neural model of RF perception based on known V4 properties that exhibits many of the characteristics of human RF perception. The model is composed of two main parts: (1) recovery of object position using large-scale non-Fourier V4-like concentric units that respond at the center of concentric contour segments across orientations, and (2) curvature detectors that encode local shape information. Each curvature mechanism combines multiplicatively the responses of three oriented filters, the positions and orientation preferences of which determine the curvature mechanism's tuning properties for position, orientation, and degree of curvature. When responding to RF patterns, peak responses occur at points of maximum curvature. Shape is represented as curvature responses as a function of orientation around the object center, and the cross-correlation of that function with a sine wave peaks when the frequency of the sine wave matches the number of peaks in the stimulus. Cross-correlation strength can be used to model human performance. Model and human performance are comparable for detection, identification, and lateral masking tasks. Moreover, the model also shows size invariance of detection performance due to scaling of the curvature mechanisms. The model is then used to make novel predictions.