This problem was successfully resolved by utilizing the following approach:
//Locate the Index of the face positioned at the center of the display
var vector = new THREE.Vector3(0, 0, 0.5);
projector.unprojectVector(vector, camera);
var raycaster = new THREE.Raycaster(camera.position, vector.sub(camera.position).normalize());
var intersects = raycaster.intersectObject(object, true);
if (intersects.length > 0) {
var index = intersects[0].faceIndex;
}
//Determine the UV Coordinates of the three vertices of the face at that specific index
var point1, point2, point3;
point1.x = objectGlobal.children[0].geometry.faceVertexUvs[0][index][0].x;
point1.y = objectGlobal.children[0].geometry.faceVertexUvs[0][index][0].y;
point2.x = objectGlobal.children[0].geometry.faceVertexUvs[0][index][1].x;
point2.y = objectGlobal.children[0].geometry.faceVertexUvs[0][index][1].y;
point3.x = objectGlobal.children[0].geometry.faceVertexUvs[0][index][2].x;
point3.y = objectGlobal.children[0].geometry.faceVertexUvs[0][index][2].y;