Although the processing within each layer of the visual hierarchy is indeed presumed to be parallel, the conventional concept of the visual hierarchy is generally described as a sequential computation progressing from lower to higher representational levels.
The present model proposes to overturn that concept of visual processing in favor of a more parallel architecture in which the computation is not thought of as progressing from one level to another, but rather the computation takes place at all levels simultaneously, which is indeed a 'more parallel processing strategy', in the vertical, as well as the horizontal sense.