1. A vision system comprising: a three-dimensional (3D) camera configured to capture a 3D image of a rearview of a dairy livestock in a stall, wherein: the dairy livestock is oriented in the 3D image with respect to: an x-axis corresponding with a horizontal dimension of the 3D image, a y-axis corresponding with a vertical dimension of the 3D image, and a z-axis corresponding with depth dimension into the 3D image; and each pixel of the 3D image is associated with a depth value along the z-axis; a memory operable to store a thigh gap detection rule set; and a processor operably coupled to the 3D camera and the memory, and configured to: obtain the 3D image; identify one or more regions within the 3D image comprising depth values greater than a depth value threshold; apply the thigh gap detection rule set to the one or more regions to identify a thigh gap region among the one or more regions, wherein the thigh gap region comprises an area between hind legs of the dairy livestock; demarcate an access region within the thigh gap region, wherein the access region is defined by: a first vertical edge, a second vertical edge, a first upper edge spanning between the first vertical edge and the second vertical edge, and a first lower edge spanning between the first vertical edge and the second vertical edge; demarcate a tail detection region, wherein the tail detection region is defined by: a third vertical edge extending vertically from the first vertical edge of the access region, a fourth vertical edge extending vertically from the second vertical edge of the access region, a second upper edge spanning between the third vertical edge and the fourth vertical edge, and a second lower edge spanning between the third vertical edge and the fourth vertical edge, wherein the second lower edge is adjacent to the first upper edge of the access region; partition the 3D image within the tail detection region along the z-axis to generate a plurality of image depth planes; examine each of the plurality of image depth planes, wherein examining each of the plurality of image depth planes comprises: identifying one or more tail candidates within the image depth plane; comparing the one or more tail candidates to a tail model; discarding tail candidates that do not correspond with the tail model; and identifying a tail candidate from among the one or more tail candidates as a tail of the dairy livestock when the tail candidate corresponds with the tail model; and determine position information for the tail of the dairy livestock in response to identifying the tail of the dairy livestock.