Rendering complex colour inside 3D printed foods : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Technology at Massey University, Palmerston North, New Zealand
Three-dimensional (3D) printing refers to a group of digitally controlled, additive
manufacturing technologies increasingly used to fabricate customised objects from a range of
possible materials, including food ingredients, using a digital image file representing the object.
A novel variation on 3D food printing is being developed to customise the appearance of foods
with an embedded 3D colour image by the selective blending of primary colorants. This
capability is beyond what is needed usually for the coloration of bulk, single food matrices.
In this thesis, non-food techniques of colorimetric matching (used in computer match
prediction) and colour gamut mapping (from cross-media colour reproduction), were
investigated as potential methods for dye recipe computation by the new 3D colour food printer.
The aim was to develop a model for transforming image RGB data to dye recipe data, taking
into account the variable effects of food properties. The two techniques were applied to the
problem of matching a set of standard tile colours using a set of primary colorants in model food
substrates. Kubelka-Munk (K-M) blending equations underlying both techniques were
developed for blends of Brilliant Blue, Ponceau 4R (red) and Tartrazine (yellow) food dyes
when added to a microwave-baked cake and to four variants of a wheat starch gel. Validation
of the model for the cake blends was shown the by ΔE*ab,10 differences between computed and
measured L*10a*10b*10 colours falling within range of a visually acceptable match (three
ΔE*ab,10 units). For some of the gel blends, the ΔE*ab,10 differences reached five units.
Dye recipes computed by a modified colorimetric matching algorithm to match target tile
colours with cake colours at times called for negative quantities, or totals that exceeded the legal
limits for foods containing dyes, indicating that the target colour was outside the range (gamut)
of the cake-dye system. In these recipes, individual negative dye quantities were increased to
zero, and totals scaled back to within the legal limit, retaining relative dye proportions. This
resulted in close differences between tile and cake before scaling (with computed ΔE*ab,10 values
of less than three units for as many as eight of the twelve target colours) becoming much larger
after scaling (up to 39 ΔE*ab,10 units), though visual inspection of the colour pairs suggested that
the matches might be closer.
The gamut of perceived colours from a coloured food is not only constrained by legal
restrictions on dye addition, but dependent on the properties of the food itself, such as its
background colour (seldom white) and the light-scattering effects of surface texture. Compared
with colour images, foods are likely to have a more limited colour gamut, the size of which is
expected to vary with changes in formulation and processing. Gamut mapping techniques were
used to investigate the extent to which the target tile colours themselves needed to be scaled
back before matching solutions and corresponding dye recipes could be computed. Using four
samples of the gel that differed only in their level of (artificial) browning, including white, the
impact of browning on the colour gamut was determined. Using the cake, solutions from gamut
mapping were compared with those from colorimetric matching.
A gamut of discrete colours is treated as a continuous volume in colour space. In the absence of
a published gamut calculation for coloured foods, a technique was developed to compute a mesh
of points on the colour gamut boundary. Boundary colours were computed using dye blends not
exceeding the legal limit, and spaced such that ΔE*ab,10 did not exceed three units. This method
was applied to the white (non-textured) gel containing dye blends, to generate a ‘base’ gamut.
The absorption behaviour of each dye was found to be largely consistent among the white and
browned gels which enabled quick computation of colour gamuts for the brown gels by
substituting the absorption spectrum of a brown gel for that of the white in the K-M equation.
The colour gamut was found to decrease in size and to shift position with increased gel
browning. The dye blends that were used to compute the colour gamut boundary for the
whitened gel were combined with the absorption spectrum for the cake to compute the gamut
boundary for the cake colours. All colour gamuts were specific to the standard D65 illuminant
and 10 degree standard observer.
In the investigation of the effects of browning, colour gamut mapping began with the initial
replacement of each tile colour with a colour from the white gel gamut. All colours were
replaced gradually by a darker, and often less chromatic, colour, as the level of browning in the
gel was increased. As a result of the reduction in gamut size with increased gel browning, the
difference between tile colours and their replacement targets in each of the reduced gamuts was
smaller for tile colours having ‘brown’ characteristics (such as Orange, Red and Yellow) than
they were for blue-, pink- and green- coloured tiles. Larger increases in total dye quantity with
increased gel browning were needed for the latter group of colours than for the former. For
most colours an increase in the relative proportion of the darkest dye in the recipe was also
needed. The actual dye quantities computed for each replacement colour depended on the
availability of mesh points in the region of colour space in which the tile was located.
Colour gamut mapping required a heavier computational load than the colorimetric matching
technique to provide solutions for tile colours in the cake-dye gamut. Although not always
giving solutions in the same angular region of colour space as the tile colours, colorimetric
matching was able to produce similar ΔE*ab,10 differences between tile colour and best cake
match as did colour gamut mapping, for not necessarily more or less total dye.
Two forms of a generalised algorithm are proposed for the computation of dye recipes by the
3D colour food printer. One algorithm is modelled on a workflow for cross-media colour
reproduction. A series of transformations that account progressively for the effect of individual
characteristics of the food printing substrate on the achievable gamut from dye blends is
incorporated into the main series of transformations that transcribes RGB image data to dye
recipe data. In the other algorithm, modelled on colorimetric matching, it is the progressive
effect of each individual characteristic on the light-absorption characteristics of the un-dyed
food printing substrate that is accounted for, and incorporated into the main matching workflow.