---
title: 'Print2Volume: Converting Media into 3D Volumes'
url: https://www.emergentmind.com/topics/print2volume
type: topic
---

# Print2Volume: Converting Media into 3D Volumes

Print2Volume denotes a class of pipelines that convert non-volumetric or partially volumetric inputs into explicit three-dimensional volume representations. In the cited arXiv literature, the term is used explicitly for a three-stage framework that generates synthetic OCT-based 3D fingerprint volumes from 2D fingerprint images, and it is also used to describe an inkjet printing-based volumetric display pipeline that converts digitally specified 3D or multi-view 2D content into a physical volumetric structure built from printed transparent films [2508.21371], [1702.00182]. Closely related systems extend the same surface-to-volume or radiance-to-volume logic to material-centric volumetric printing and to assemblable volumetric partitioning for fabrication [2503.00887], [1904.10213].

## 1. Scope and principal formulations

The literature presents Print2Volume as a conversion problem rather than a single device class. In one formulation, the input is a binary or grayscale 2D fingerprint and the output is a realistic OCT-like 3D fingerprint volume with subsurface anatomy and imaging artifacts. In another, the input is digital 3D content or several 2D patterns and the output is a stack of printed fluorescent layers that emits a volumetric image under UV excitation. Related fabrication papers use the same surface-to-volume idea to map radiance fields or segmented surfaces into printable volumetric structures [2508.21371], [1702.00182], [2503.00887], [1904.10213].

| Manifestation | Input and output | Core mechanism |
|---|---|---|
| Print2Volume [2508.21371] | 2D fingerprint image $\rightarrow$ OCT-based 3D fingerprint volume | 2D style transfer, 3D Structure Expansion Network, OCT Realism Refiner |
| Inkjet printing-based volumetric display [1702.00182] | 3D or multi-view 2D content $\rightarrow$ physical volumetric display | fluorescent inks printed on stacked transparent films |
| DreamPrinting [2503.00887] | radiance-based volumetric representation $\rightarrow$ Volumetric Printing Primitives | Kubelka-Munk calibration, concentration inversion, 3D stochastic halftoning |
| Surface2Volume [1904.10213] | surface-segmented mesh $\rightarrow$ volumetric parts and assembly plan | assembly trajectories, partition topology, interface geometry |

This scope already separates Print2Volume from purely surface-oriented pipelines. The emphasis falls on explicit volumetric state variables: printed voxels, OCT voxels, volumetric printing primitives, or tetrahedrally partitioned parts. A plausible implication is that Print2Volume is best understood as a design pattern for compiling geometric, optical, or biometric information into an operational 3D volume.

## 2. Inkjet-printed volumetric display as a physical Print2Volume pipeline

The 2017 volumetric display prototype realizes Print2Volume in a literal fabrication sense. Printed points of fluorescent ink are treated as physical voxels, and a volumetric display is formed by stacking many transparent films, each carrying a 2D pattern; the ensemble of all printed pixels in the stack constitutes a discrete 3D distribution of luminescent material [1702.00182]. The prototype uses transparent polymer films, specifically 0.1 mm polyester; fluorescent inks with red, green, and blue dyes; and acrylic spacers. The fluorescent channels are red europium complex, green β‑quinophthalone dye, and blue coumarin derivatives, with quantum yields
\[
\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.
\]
A commercial inkjet printer deposits these inks onto each film, the films are stacked into 20 layers with 0.5 mm spacing, and the effective volume is about \(35 \,\text{mm} \times 35 \,\text{mm} \times 12.5 \,\text{mm}\). UV sources at 365 nm placed around the display excite the inks, producing a self-luminous 3D image with motion parallax.

For direct 3D image printing, a 3D point \((O_x,O_y,O_z)\) is mapped to the nearest slice \(Z_n\) and printed at \((u,v)=(O_x,O_y)\). The paper formalizes this as
\[
(u,v,n) = f(O_x,O_y,O_z)
= \left(\text{round}(O_x / s_x),\, \text{round}(O_y / s_y),\, \arg\min_n |O_z - Z_n|\right).
\]
For view-dependent multi-pattern encoding, the voxel rule is multiplicative. If \(A,B,C\) are target full-colour patterns associated with different projection directions, then
\[
V(x, y, z) = a(u_A, v_A) \cdot b(u_B, v_B) \cdot c(u_C, v_C),
\]
with component-wise multiplication over RGB channels. The projected view along, for example, pattern \(A\)’s direction is
\[
a'(u_A, v_A) = \sum_{(x,y,z) \in P_A(u_A,v_A)} V(x,y,z),
\]
which factors into the original pixel multiplied by a background term. This is the analytical basis for storing several recognizable 2D patterns in one 3D emissive material distribution.

The paper reports a full-colour 3D flower/butterfly prototype with 51,767 full-colour points and 300 × 300 pixels per layer, and multi-pattern prototypes with three and four different viewpoints. Simulations show recognizable three-pattern and four-pattern reconstructions, but the physical prototypes exhibit blur and contrast loss because each polyester film has approximately 82% transmittance at 365 nm and approximately 90% transmittance in the visible. After 20 films, the UV intensity is approximately \(0.82^{20} \approx 0.02\). This identifies transparency, scattering, and coarse depth sampling as the dominant scaling limits. The paper nevertheless positions the method for digital signage, media art, entertainment, and security [1702.00182].

## 3. Print2Volume for synthetic OCT-based 3D fingerprint generation

The 2025 paper titled “Print2Volume: Generating Synthetic OCT-based 3D Fingerprint Volume from 2D Fingerprint Image” defines the term as a generative framework for biometric data synthesis [2508.21371]. The motivation is the scarcity of large-scale public OCT fingerprint data: OCT captures internal fingerprint structure, viable epidermis / dermis junction information, and sweat gland morphology, but OCT devices are bulky and expensive, acquisition is time-consuming, and the public ZJUT‑EIFD dataset has only 2,714 samples from 399 fingers.

The framework operates in three sequential stages. The first stage is a 2D style transfer module that converts a binary fingerprint into a grayscale image mimicking the style of a Z-direction mean-projected OCT scan. The implementation uses MATEBIT, with Contrastive Style Learning
\[
\mathcal{L}_{\text{style}}
= - \log \frac{\exp(z \cdot z^+ / \tau)}{\sum_j \exp(z \cdot z_j / \tau)}.
\]
The second stage is a 3D Structure Expansion Network, a 2D-to-3D encoder-decoder that maps the grayscale en-face fingerprint \(I_s\) to a structural volume \(V_E \in \mathbb{R}^{D \times H \times W}\), typically \(D=32, H=W=256\). Its loss is
\[
\mathcal{L}_E = \text{BCE}(V_{real}, G_E(I_s)) + \text{3D-SSIM}(V_{real}, G_E(I_s)).
\]
The third stage is an OCT Realism Refiner based on a 3D GAN, with a 3D U-Net generator and 3D PatchGAN discriminator. The adversarial and reconstruction objective is
\[
\mathcal{L}_G = \mathcal{L}_{\text{adv}} + \alpha \|V_{real} - V_R\|_1,\quad
\mathcal{L}_D = \mathcal{L}_{\text{adv}},
\]
with \(\alpha = 10\).

Training is fully supervised and paired on ZJUT‑EIFD-derived data. The synthetic 2D source is PrintsGAN plus a custom autoencoder trained with \(L2\) loss on 10k ground-truth binary fingerprints. The final synthetic corpus contains 28,000 identities with 15 impressions per identity, yielding 420,000 volumes. Distributional similarity improves substantially after refinement: FVD\(_{\text{I3D}}\) decreases from 2945.5 for the 3D Structure Expansion output \(V_E\) to 1564.6 for the refined OCT volume \(V_R\), and FID decreases from 94.15 to 67.45. In recognition experiments on ZJUT‑EIFD, self-build training only yields an Equal Error Rate of 15.62%, synthetic training only yields 3.51%, and synthetic pre-training plus self-build fine-tuning yields 2.50%; TAR at FAR=0.1% improves from 78.95 to 99.12, and TAR at FAR=0.01% improves from 51.35 to 95.10 [2508.21371].

The paper also notes an important internal distinction: the structural volume \(V_E\) is often cleaner than the refined OCT-like volume \(V_R\). This makes \(V_E\) useful as a potential source of high-quality labels for internal fingerprint reconstruction and dermal/epidermal contour detection, while \(V_R\) better matches real OCT data distribution.

## 4. Volume computation and inversion as computational infrastructure

Several adjacent papers explicitly place their methods in a Print2Volume context by treating volumization as a computational problem: converting surfaces, scalar fields, or segmented medical volumes into exact or efficiently queryable volume values. One route begins with Marching Cubes. The divergence-theorem method for partial cell volume in Cartesian coordinates chooses \(\vec{f}=(x,y,z)^T\), so \(\nabla\cdot\vec{f}=3\), and obtains
\[
\text{Volume}(\Omega)
= \frac{1}{3}\oint_{\partial\Omega} \vec{n}\cdot(x,y,z)\, dS
= \frac{1}{6}\sum_T (\vec{N}_T\cdot \vec{x}_{c,T}),
\]
for a closed triangulated surface. The paper provides triangulation templates for 23 unique Marching Cubes configurations, reports exactness for planar interfaces, and shows second-order accuracy on a sphere benchmark, with volume error decreasing from 0.18462996 on a 10×10×10 mesh to 0.00342889 on an 80×80×80 mesh [1308.0387].

A second route couples Marching Cubes to a 3D Binary Indexed Tree. The 2024 medical-imaging paper stores per-cube intrinsic volume contributions in a Fenwick tree, enabling \(O(\log N \log M \log P)\) updates and region queries while reconstructing volumetric CT/MR objects. The method uses 30 configurations of volume values derived from polygonal mesh generation and reports deviations within \(\pm 0.004 \text{cm}^3\) on test objects, while preserving interactive subregion queries for slicing and editing [2412.10441]. A third route, Front2VOF, clips triangular interface elements to a Cartesian cube and computes the enclosed volume exactly using Gauss’s and Green’s theorems. For a unit cube, the color function is the local volume fraction \(C=V_{\text{inside}}\), and validation shows machine-precision agreement for plane-interface tests and approximately second-order convergence for triangulated spheres [2501.04744].

Grid discretization provides a different volumization strategy. Wolumes computes atom and residue volumes in proteins by sampling a regular grid with spacing \(D\), typically \(D=0.75\ \text{Å}\), assigning grid points to van der Waals spheres with equal sharing in overlap regions, and summing \(D^3\) contributions. The paper recommends \(D=0.75\ \text{Å}\) as a compromise between speed and accuracy, reports approximately 4.2% error relative to a \(D=0.1\ \text{Å}\) reference, and gives empirical runtime laws such as
\[
\text{Time} = 0.014\, n_{\text{ato}} + 4.22 \cdot 10^{-6}\, n_{\text{ato}}^2
\]
at fixed \(D=0.75\ \text{Å}\) [1406.3242]. These methods do not fabricate volume, but they formalize a recurring Print2Volume requirement: robust conversion of non-volumetric or partially volumetric descriptions into explicit volumetric quantities.

## 5. Material-centric volumetric printing and volumetric primitives

DreamPrinting generalizes Print2Volume to material-aware fabrication from radiance fields. Its goal is to transform radiance-based volumetric representations such as NeRF, OpenVDB volumes, and TRELLIS-generated radiance fields into explicit, material-centric Volumetric Printing Primitives (VPPs), where every voxel is assigned a single printable pigment while preserving geometry, colour, translucency, and internal structure [2503.00887]. The hardware model is a Stratasys J850 Prime full-colour PolyJet printer with six pigments \(\{C,M,Y,K,W,Cl\}\), and the final output is a discrete pigment label per voxel.

The physical bridge is the Kubelka–Munk model. For a pigment concentration vector \(C=\{c_i\}\),
\[
K_C(\lambda) = \sum_{i\in I} c_i K_i(\lambda),\quad
S_C(\lambda) = \sum_{i\in I} c_i S_i(\lambda),
\]
and the reflectance and transmittance at thickness \(t\) are
\[
R_C(\lambda) = \frac{\sinh(b S_C(\lambda) t)}{a \sinh(b S_C(\lambda) t) + b \cosh(b S_C(\lambda) t)},
\]
\[
T_C(\lambda) = \frac{b}{a \sinh(b S_C(\lambda) t) + b \cosh(b S_C(\lambda) t)},
\]
with \(a = \frac{S_C(\lambda)+K_C(\lambda)}{S_C(\lambda)}\) and \(b=\sqrt{a^2-1}\). These spectral functions are converted to RGB under \(D_{65}\), and a scalar density \(\sigma_C\) is fit to the transmittance profile by approximating \(T_{\text{approx}}(t)\approx \exp(-\sigma_C t)\). DreamPrinting then inverts this continuous colour-density target to pigment concentrations and applies a 3D stochastic halftoning procedure so that each voxel receives exactly one pigment label.

The paper reports that this pipeline reproduces semi-transparent structures such as fur, leaves, and clouds, and that the density approximation error is small enough to support a NeRF-compatible scalar-opacity model. It also formalizes a stringent hardware constraint that distinguishes DreamPrinting from ordinary volume rendering: a volumetric rendering primitive may carry continuous \((r,g,b,\sigma)\), but the printer can deposit only a single material label at each voxel [2503.00887]. This is a material-centric Print2Volume formulation rather than a display-centric or biometric one.

## 6. Surface-conforming partitioning, applications, and limitations

Surface2Volume addresses a different but complementary volumization problem: transforming a surface-segmented object into volumetric parts that conform to the input segmentation and can be moved apart with no collisions [1904.10213]. The algorithm explicitly solves for three types of variables—per-part assembly trajectories, partition topology, and interface geometry—and does so in sequence: first computing the assembly trajectories, then determining interface topology, and finally computing interface locations that allow parts assemblability. The discrete optimization is performed on a tetrahedralization of the object volume, and assemblability is restricted to linear trajectories. When a single-stage partition is impossible, the method identifies inputs that necessitate sequential assembly and partitions these inputs gradually by computing and disassembling a subset of assemblable parts at a time.

Across the cited literature, applications are correspondingly diverse. The inkjet volumetric display is proposed for digital signage, media art, entertainment, and security [1702.00182]. The OCT Print2Volume framework is positioned as a response to data scarcity in OCT-based biometrics, enabling large-scale pre-training for recognition and providing clean intermediate structural volumes for annotation-heavy tasks [2508.21371]. DreamPrinting targets high-fidelity 3D printing of volumetric radiance content, especially semi-transparent structures [2503.00887]. Surface2Volume supports fabrication of multi-attribute objects by producing single-attribute volumetric parts that can be fabricated separately and assembled [1904.10213].

The limitations are equally domain-specific. The stacked-film display suffers from UV attenuation, visible absorption and scattering, blur due to refraction and diffusion at film interfaces, and relatively low z-resolution [1702.00182]. The fingerprint framework still faces a domain gap, depends on the diversity of the initial 2D fingerprints, and uses implicit rather than explicit anatomical modeling [2508.21371]. DreamPrinting is hardware-specific, limited by the printer’s fixed pigment set and single-material-per-voxel constraint, and relies on offline spectral calibration [2503.00887]. Surface2Volume assumes rigid parts and linear extraction trajectories and is sensitive to mesh resolution and segmentation patterns [1904.10213]. This suggests that Print2Volume is not a single mature technology stack but a family of domain-specific strategies for making volumetric structure explicit, computable, and usable.

Source: https://www.emergentmind.com/topics/print2volume