Print2Volume: Converting Media into 3D Volumes

• Print2Volume is a design pattern that transforms non-volumetric or partially volumetric inputs, such as 2D images, into explicit 3D volumes through multi-stage computational pipelines.
• It spans diverse applications—from synthetic OCT fingerprint volume generation to inkjet-printed volumetric displays—by leveraging methods like 2D style transfer, 3D structure expansion, and view-dependent encoding.
• Innovations include robust volumization, material-centric printing, and precise assembly partitioning, though challenges such as UV attenuation, resolution limits, and hardware constraints remain.

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 (Miao et al., 29 Aug 2025, Hirayama et al., 2017). 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 (Wang et al., 2 Mar 2025, Araújo et al., 2019).

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 (Miao et al., 29 Aug 2025, Hirayama et al., 2017, Wang et al., 2 Mar 2025, Araújo et al., 2019).

Manifestation	Input and output	Core mechanism
Print2Volume (Miao et al., 29 Aug 2025)	2D fingerprint image $\rightarrow$ OCT-based 3D fingerprint volume	2D style transfer, 3D Structure Expansion Network, OCT Realism Refiner
Inkjet printing-based volumetric display (Hirayama et al., 2017)	3D or multi-view 2D content $\rightarrow$ physical volumetric display	fluorescent inks printed on stacked transparent films
DreamPrinting (Wang et al., 2 Mar 2025)	radiance-based volumetric representation $\rightarrow$ Volumetric Printing Primitives	Kubelka-Munk calibration, concentration inversion, 3D stochastic halftoning
Surface2Volume (Araújo et al., 2019)	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 (Hirayama et al., 2017). 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 $\rightarrow$0 are target full-colour patterns associated with different projection directions, then

$\rightarrow$1

with component-wise multiplication over RGB channels. The projected view along, for example, pattern $\rightarrow$2’s direction is

$\rightarrow$3

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 $\rightarrow$4. 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 (Hirayama et al., 2017).

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 (Miao et al., 29 Aug 2025). 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

$\rightarrow$5

The second stage is a 3D Structure Expansion Network, a 2D-to-3D encoder-decoder that maps the grayscale en-face fingerprint $\rightarrow$6 to a structural volume $\rightarrow$7, typically $\rightarrow$8. Its loss is

$\rightarrow$9

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

$\rightarrow$0

with $\rightarrow$1.

Training is fully supervised and paired on ZJUT‑EIFD-derived data. The synthetic 2D source is PrintsGAN plus a custom autoencoder trained with $\rightarrow$2 loss on 10k ground-truth binary fingerprints. The final synthetic corpus contains 28,000 identities with 15 impressions per identity, yielding 420,000 volumes. Distributional similarity improves substantially after refinement: FVD$\rightarrow$3 decreases from 2945.5 for the 3D Structure Expansion output $\rightarrow$4 to 1564.6 for the refined OCT volume $\rightarrow$5, 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 (Miao et al., 29 Aug 2025).

The paper also notes an important internal distinction: the structural volume $\rightarrow$6 is often cleaner than the refined OCT-like volume $\rightarrow$7. This makes $\rightarrow$8 useful as a potential source of high-quality labels for internal fingerprint reconstruction and dermal/epidermal contour detection, while $\rightarrow$9 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 $\rightarrow$0, so $\rightarrow$1, and obtains

$\rightarrow$2

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 (Wang, 2013).

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 $\rightarrow$3 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 $\rightarrow$4 on test objects, while preserving interactive subregion queries for slicing and editing (Nguyen-Le et al., 2024). 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 $\rightarrow$5, and validation shows machine-precision agreement for plane-interface tests and approximately second-order convergence for triangulated spheres (Pan et al., 8 Jan 2025).

Grid discretization provides a different volumization strategy. Wolumes computes atom and residue volumes in proteins by sampling a regular grid with spacing $\rightarrow$6, typically $\rightarrow$7, assigning grid points to van der Waals spheres with equal sharing in overlap regions, and summing $\rightarrow$8 contributions. The paper recommends $\rightarrow$9 as a compromise between speed and accuracy, reports approximately 4.2% error relative to a $$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$0 reference, and gives empirical runtime laws such as

$$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$1

at fixed $$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$2 (Carugo, 2014). 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 (Wang et al., 2 Mar 2025). The hardware model is a Stratasys J850 Prime full-colour PolyJet printer with six pigments $$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$3, and the final output is a discrete pigment label per voxel.

The physical bridge is the Kubelka–Munk model. For a pigment concentration vector $$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$4,

$$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$5

and the reflectance and transmittance at thickness $$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$6 are

$$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$7

$$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$8

with $$\Phi_R = 0.43,\quad \Phi_G = 0.85,\quad \Phi_B = 0.89.$$9 and $$35 \,\text{mm} \times 35 \,\text{mm} \times 12.5 \,\text{mm}$$0. These spectral functions are converted to RGB under $$35 \,\text{mm} \times 35 \,\text{mm} \times 12.5 \,\text{mm}$$1, and a scalar density $$35 \,\text{mm} \times 35 \,\text{mm} \times 12.5 \,\text{mm}$$2 is fit to the transmittance profile by approximating $$35 \,\text{mm} \times 35 \,\text{mm} \times 12.5 \,\text{mm}$$3. 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 $$35 \,\text{mm} \times 35 \,\text{mm} \times 12.5 \,\text{mm}$$4, but the printer can deposit only a single material label at each voxel (Wang et al., 2 Mar 2025). 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 (Araújo et al., 2019). 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 (Hirayama et al., 2017). 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 (Miao et al., 29 Aug 2025). DreamPrinting targets high-fidelity 3D printing of volumetric radiance content, especially semi-transparent structures (Wang et al., 2 Mar 2025). Surface2Volume supports fabrication of multi-attribute objects by producing single-attribute volumetric parts that can be fabricated separately and assembled (Araújo et al., 2019).

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 (Hirayama et al., 2017). 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 (Miao et al., 29 Aug 2025). DreamPrinting is hardware-specific, limited by the printer’s fixed pigment set and single-material-per-voxel constraint, and relies on offline spectral calibration (Wang et al., 2 Mar 2025). Surface2Volume assumes rigid parts and linear extraction trajectories and is sensitive to mesh resolution and segmentation patterns (Araújo et al., 2019). 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.