from these standard shapes and sizes to justify the cost 
and effort of custom-built shoe lasts and made-to-measure 
shoes. The mensuration task increases with the extent of 
this variation. 
2 To determine this foot shape whilst it is subject to 
normal load. Even a cursory inspection will confirm 
that our feet change shape significantly as we stand 
up, and clearly it is this latter shape that is required 
for shoe-making. To measure feet in anything other 
than a standing position seems to me to be almost 
totally useless for this purpose. 
3 The measurement must be done quickly. Standing 
is not a totally passive activity, even when we are 
standing still out feet have to move sufficiently for 
us to maintain our balance. My layman's estimate 
is that we should complete our measurements in 
less than one tenth of a second, so the best accuracy 
requires something very close to simultaneous 
determination of all points to be fixed. 
4 In line with my aim of putting the whole process in 
the hands of the users, it is important that the most 
economical solution be found. This includes a 
reasonable balance between capital cost and the 
amount of time taken to measure and process the 
data. 
My experiments so far have been on the assumption that 
photogrammetry would be the appropriate mensuration 
technique. The various traditional advantages of close- 
range photogrammetry for this sort of measuring work are 
still attractive. They include speed of capture, completen- 
ess, low costs for original photography, and the long-term 
stability of the stored record (the photograph itself). The 
requirement of a low-cost system has led me to plan on the 
manual digitising of (enlarged) photographs as in the 
Rollie and Wild-Leica systems. For reasons described 
elsewhere (Gordon 1991) I have chosen to concentrate on 
the use of mirrors to provide simultaneous multi-station 
exposures of the object. This approach is not new (Kratky, 
1975; Keys, et al, 1975; Torlegaard, 1975) and offers a 
number of advantages. The mirrors automatically give 
simultaneous multistation exposures without any possibility 
of a partial failure in the synchronisation. A single flash 
unit can illuminate all the views, via the same mirrors that 
provide the multiple images. What is more it is quite easy 
to make the mirror system as robust as necessary. The 
layout of the mirrors was designed to provide at least 3 
different views of each point. As can be seen from Figure 
1, the view from each mirror is effectively a separate 
exposure from different 'camera' positions. As all the 
mirrors are vertical (or nearly so), each of these 'cameras' 
is tilted down from the horizontal by about the same 
amount as the real camera =15°. 
  
"Camera "I 
+ 
CAMERA 
t 
"Camera" II — X 
X II “Camera” IV 
Camera” II 
Figure 1. Planimetric layout of foot, camera station, 4 
mirrors, and 4 psuedo camera stations 
The determination of these 'camera' positions, and the 
positions of targets identified in two or more 'photographs, 
is classical close-range photogrammetry. While a number 
of solutions are possible (e.g. Granshaw, 1980), I have been 
using a bundle adjustment which is part of a suite called 
General Adjustment Programme (GAP) developed by Dr 
Jerry Clark at City University in London. I am pleased 
and grateful to have Dr Clark's permission and support. 
Because of the divergent 'camera' angles involved, the 
possible targetting options led almost inevitably to spherical 
targets. Their prime advantage is that they remain regular 
and symmetric from every viewpoint. The most successful 
of these were some 3mm diameter dressmaking beads. 
Once mounted on a pin or cotton thread, and painted matt 
white, these proved to be the most satisfactory of all. 
While not perfectly spherical they presented a symmetrical 
image from all viewpoints, all with a common centre. The 
only retro-reflective targets I could find, or construct from 
reflective tape, were hard to find (let alone maeasure to) 
at the low angles of incidence they had in some of the 
views. The ideal target has a photographic image that 
presents an annulus around the measuring mark. Trinder 
(1971) advises that this annulus should be some 25 pm at 
photo scale where the optical enlargement is 10x, reducing 
to 15pm with clear high contrast images. With a 25pm 
measuring mark this implies a 75pm target, which scales up 
to 2.1mm for the most distance object point. All the 
targets I tried were larger than this optimum size, and this 
was exacerbated when their object distance were as much 
as 2.5x less than the maximum object distance. Most hand 
  
    
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