normal segment at a certain point A on the envelope 
surface. By analogy, taking all the points on the tumor 
envelope  as  the  starting  point,  each  point  on  the 
envelope surface is made perpendicular to the normal 
segment of the tangent plane Σi at the point, the length 
of the normal segment is set as 1cm per unit length, 
and finally a new convex surface composed of the end 
point of the unit length normal segment is obtained, 
so that the new convex surface is defined as a tangent 
edge surface 1cm away from the tumor outer network, 
and its principle is regarded as the uniform expansion 
deformation  of  the  tumor  model.  In  summary,  the 
outward  expansion  deformation  is  based  on  all  the 
points  on  the  envelope  surface,  and  the  convex 
surface that expands and deforms by 1 cm is defined 
as the tangent edge surface of the tumor. The distance 
from any point on the cut edge surface to the tumor 
should be no less than 1 cm, as shown in Fig. 2(a).   
Finally, based on  the envelope surface isometric 
expansion  to  obtain  a  plurality  of  convex  surfaces, 
consisting  of  a  plurality  of  progressively  deformed 
and expanded convex surfaces of the field, we define 
it  as  the  margin  field  of  the  tumor,  wherein  the 
interval between each surface of the margin field is 1 
cm, as shown in Figure 2 (b), the distance from the 
above-mentioned  cut  edge  surface  to  the  tumor 
surface contour is  1  cm, the cut  edge  surface is  the 
tumor 1 cm margin field. 
 
 
(a)                               (b)                                  (c) 
Figure 2: The outer contour surface, envelope surface, and marginal field of the tumor. 
3.2  Distance Calculation Application 
Between Scalpel and Tumor Based 
on Margin Margin Field 
In the future minimally invasive liver tumor resection, 
robot technology will be continuously introduced for 
the requirements of accurate removal of liver tumors, 
and  under  the  motion  simulation  model  based  on 
robot surgical action, the definition and visualization 
of  the  margin field  provide  the  robot  with  distance 
parameters to know the distance d of the scalpel and 
the  tumor  boundary.  According  to  the  distance 
between the margin field and the envelope surface, it 
is named, as shown in Fig. 2(c). Such as 1cm margin 
field,  2cm  margin  field  and  3cm  margin  field,  etc. 
Assuming that the scalpel head is located between the 
2cm to 3cm margin field in the simulation model of 
robot motion, it is obvious that the distance from the 
scalpel head to the tumor is 2 to 3cm. In summary, the 
definition  of  marginal  field  can  be  used  in  future 
robotic  minimally  invasive  surgery  to  measure  the 
distance  between  the  scalpel  and  the  intrahepatic 
tumor,  providing  auxiliary  guidance  for  physicians 
when  removing  the  tumor  during  surgery,  and 
avoiding  the  risk  of  surgery  caused  by  the  scalpel 
touching the tumor. 
3.3 
Establishment System for Marginal 
Fields 
Fig.  3  Further  provides  an  establishing  module  for 
tumor margin margin field, comprising: establishing 
module 1, determining module 2, envelope creation 
module  3  and  determining  module  4.  Wherein,  the 
establishment of module 1 for obtaining the patient's 
imaging  data,  through  the  three-dimensional 
reconstruction of the body data to obtain a model of 
the relative position relationship between the tissues; 
judgment  module  2, for calling  the relative position 
information between the tumor and other tissues to 
determine  the  resectability  of  the  tumor,  if  yes 
(intrahepatic  tumor  has  resectability),  into  the 
envelope creation module 3, if not, end; the envelope 
creation  module  is  used  to  establish  an  envelope 
surface according to the external contour information 
of  the  tumor  surface,  the  envelope  surface  is  the 
convex envelope of the tumor; determine module 4, It 
is used to determine the tumor 1 cm margin and 
margin
 field based on the envelope surface of the