---
title: 'ImplMORe: Implicit 3D Organ Reconstruction'
url: https://www.emergentmind.com/topics/implmore
type: topic
---

# ImplMORe: Implicit 3D Organ Reconstruction

ImplMORe is an end-to-end deep learning method for reconstructing fine-grained 3D organ surfaces directly from volumetric medical images by learning a continuous occupancy function rather than relying on explicit voxel, mesh, or point-cloud representations. In the reported formulation, a 3D CNN encoder supplies multi-scale local image features, trilinear interpolation lifts those features into the continuous domain at arbitrary spatial coordinates, and an implicit decoder predicts occupancy values whose $0.5$-level set defines the reconstructed surface. The method is applied to single-organ and multi-organ reconstruction on the TotalSegmentator dataset, where it is reported to outperform discrete explicit-representation baselines while producing surfaces at a resolution higher than the input image resolution [2509.12068].

## 1. Representational premise

ImplMORe is built around an implicit surface model. Instead of directly predicting a dense voxel occupancy grid, a mesh topology, or a point set, it learns a continuous function
$$
f:\mathbb{R}^3 \longrightarrow [0,1]
$$
that maps a spatial point $\mathbf{p}=(x,y,z)$ to an occupancy probability. Points with $f(\mathbf{p})>0.5$ are classified as inside the organ, and the organ surface is represented by the $0.5$-level set. This formulation is central to the method’s ability to recover surface detail beyond the native voxel resolution of the input volume [2509.12068].

The paper explicitly positions ImplMORe against conventional explicit representations—voxels, meshes, and point clouds. The stated motivation is that explicit representations are constrained by image resolution, and higher-resolution explicit outputs require more memory and compute. By contrast, a continuous occupancy function permits evaluation on arbitrarily dense query grids at inference time. The paper characterizes this as a continuous and differentiable shape model with “virtually unlimited output resolution, constrained only by sampling density.”

A further consequence of the representation is that surface extraction is decoupled from network output resolution. The network predicts occupancy at queried coordinates, and surface geometry is recovered afterward with Marching Cubes. This separates shape representation from the discretization used during training or inference. A plausible implication is that the method is especially suited to anatomical structures whose clinically relevant geometry is dominated by boundary fidelity rather than volumetric label accuracy alone.

## 2. Architecture and multi-organ parameterization

ImplMORe begins with a 3D CNN encoder inspired by the encoder half of a 3D U-Net. Given an input CT volume $I\in\mathbb{R}^{D\times H\times W}$, five successive convolutional blocks produce multi-scale feature volumes $F_1,\dots,F_5$. Each block contains two $3\times3\times3$ convolutions, batch normalization, and ReLU activations, followed by a $2\times2\times2$ max-pool that halves spatial resolution and doubles channel count. Early layers are intended to retain local high-frequency texture, whereas deeper layers encode broader anatomical context [2509.12068].

To evaluate occupancy at an arbitrary point $\mathbf p$, the method does not use only the deepest feature map. Instead, it interpolates every feature scale at that point:
$$
f_i(\mathbf p)=\mathrm{TriInterp}(F_i,\mathbf p),
$$
then concatenates the interpolated descriptors,
$$
\mathbf h(\mathbf p)=\bigl[f_1(\mathbf p),f_2(\mathbf p),\dots,f_5(\mathbf p)\bigr]^\top.
$$
This multi-scale feature interpolation is the mechanism by which continuous coordinates acquire both local and global image context.

The implicit surface module is an MLP implemented as a stack of $1$D convolutions with kernel width $1$. It maps the concatenated descriptor to an occupancy probability,
$$
\hat o=f_\theta(\mathbf h(\mathbf p))\in[0,1].
$$
For multi-organ reconstruction, the paper provides two variants. In the Single-Decoder variant, a single MLP outputs one channel per organ plus background, followed by a softmax. In the Multi-Decoder variant, each organ has its own binary MLP predicting a scalar occupancy. The paper states that the Multi-Decoder design avoids conflicts when multiple organs come into contact or share boundaries, because each organ surface is modeled independently.

Each per-organ decoder has four fully connected layers. The hidden dimension is $256$ for multi-organ reconstruction and $512$ for single-organ reconstruction. This architectural asymmetry reflects the different output semantics of the two settings: a single-organ decoder can concentrate capacity on one shape, whereas the multi-organ configuration distributes modeling across organ-specific binary predictors.

## 3. Mathematical formulation, supervision, and geometric behavior

The learned occupancy function is written as
$$
f(\mathbf p)=\sigma\bigl(g_\theta(\mathbf h(\mathbf p))\bigr),
$$
with $\sigma(\cdot)$ the sigmoid activation. Training is supervised with occupancy labels sampled at query points. For a set of $n$ points $\{\mathbf p_j\}$ with binary occupancies $\{o_j\}$, the multi-decoder variant uses a binary cross-entropy loss for each organ and sums across organs [2509.12068].

In the single-decoder multi-class case, categorical cross-entropy is used instead. The paper also allows standard weight decay,
$$
\mathcal L_{\mathrm{reg}}=\lambda\|\theta\|_2^2.
$$
No explicit geometric priors such as curvature regularization are imposed. The reported claim is that smooth, watertight surfaces emerge implicitly through dense sampling near the surface and through interpolation of multi-scale image features.

That absence of explicit geometric priors is methodologically important. ImplMORe does not hand-code shape smoothness through a dedicated surface regularizer; instead, geometry is expected to arise from occupancy regression against continuous-space samples. This suggests a design philosophy closer to function learning than to traditional deformable-model optimization. The reported outcome is the absence of mesh artifacts and spurious holes in qualitative comparisons, although the paper also notes that rare topological errors may occur if organs touch.

## 4. Data preparation, sampling, optimization, and mesh extraction

The reported experiments use the TotalSegmentator dataset, described as containing 581 abdominal CT scans with 104 organ labels. For single-organ experiments, only volumes containing the full liver are retained. For multi-organ experiments, volumes containing both liver and pancreas are used. The train/validation/test split is 291/116/174. Each CT is intensity-normalized with z-score normalization, then either downsampled to $128^3$ voxels for whole-volume training or padded to $500^3$ and trained patch-wise with $128^3$ patches [2509.12068].

High-resolution ground-truth meshes are generated from original segmentation masks using Marching Cubes followed by Laplacian smoothing. These meshes serve two purposes: they provide boundary samples and enable more accurate sub-voxel occupancy labels than those obtained directly from the discretized mask.

The sampling policy is explicitly surface-aware. For single-organ reconstruction, each volume contributes 300 k query points: 200 k sampled uniformly in the organ bounding box and 100 k sampled in a narrow band around the mesh surface by jittering vertices by $\pm 0.1$ mm. For multi-organ reconstruction, each sample uses 400 k points: 200 k uniform and 200 k near the surface, split as 100 k per organ. Each mini-batch contains $b$ volumes or patches, each with $n$ points, yielding $b\times n$ training samples per iteration.

Optimization uses Adam with an initial learning rate of $1\mathrm e{-4}$, an exponential decay schedule over 200 epochs, and weight decay $\lambda=1\mathrm e{-5}$. Affine augmentations are applied jointly to the input volume and sampled query points: random translation, rotation up to $\pm 15^\circ$, and scaling between $0.9$ and $1.1$. At inference time, occupancy is evaluated either on the whole volume or on overlapping $128^3$ patches. The evaluation grid can reach $256^3$ for whole-volume inference or $1024^3$ for patch-wise inference after Hann-window blending, and Marching Cubes extracts the final $0.5$ iso-surface.

## 5. Experimental protocol and reported results

The evaluation focuses on liver reconstruction in the single-organ setting and liver-plus-pancreas reconstruction in the multi-organ setting. Reported metrics are 90% Hausdorff Distance (HD, mm), Average Symmetric Surface Distance (ASSD, mm), Intersection over Union (IoU, %), and Chamfer Distance (CD, $\times 10^{-3}$). Baselines are 3D U-Net segmentation followed by Marching Cubes, Voxel2Mesh, and Voxel2Mesh* with reduced regularization to boost detail [2509.12068].

| Setting | Method | Reported performance |
|---|---|---|
| Liver, $128^3$ | U-Net | HD 10.4 ± 4.8 mm; ASSD 4.9 ± 1.4 mm; IoU 76.7 ± 4.2%; CD 0.10 ± 0.30 |
| Liver, $128^3$ | Voxel2Mesh | HD 12.3 ± 10.8 mm; ASSD 5.4 ± 2.0 mm; IoU 83.3 ± 5.4%; CD 0.70 ± 1.50 |
| Liver, $128^3$ | ImplMORe | HD 6.5 ± 3.6 mm; ASSD 2.6 ± 1.0 mm; IoU 86.9 ± 4.7%; CD 0.03 ± 0.04 |
| Pancreas in multi-organ setting, $128^3$ | U-Net | HD 67.8 ± 28.7 mm; ASSD 18.6 ± 11.9 mm; IoU 8.1 ± 11.3%; CD 1.8 ± 2.2 |
| Pancreas in multi-organ setting, $128^3$ | ImplMORe | HD 16.0 ± 10.9 mm; ASSD 5.6 ± 2.6 mm; IoU 34.2 ± 15.1%; CD 0.14 ± 0.20 |
| Pancreas, patch-wise high resolution | ImplMORe | HD 9.3 mm; ASSD 3.3 mm; IoU 53.8% |

These results are presented in the paper as evidence that the implicit representation is especially advantageous for fine structures. The pancreas is the clearest example: in the multi-organ setting, patch-wise high-resolution training reduces HD from 16.0 mm to 9.3 mm and ASSD from 5.6 mm to 3.3 mm, while increasing IoU to 53.8%. Qualitatively, the reported improvements include sharper sulci and fissures on the liver surface, more accurate delineation of the pancreas tail and head, and the absence of mesh artifacts and spurious holes.

The paper further states that details invisible at $128^3$ voxel resolution can be recovered through continuous occupancy interpolation. This is not merely a post-processing claim: the recovered geometry is tied to the learned occupancy field and the continuous feature interpolation scheme.

## 6. Advantages, limitations, and extensions

The reported advantages of ImplMORe are threefold. First, the representation is continuous and differentiable, allowing output resolution to be increased independently of the input sampling grid. Second, the memory footprint is compact: the paper attributes this to storing only encoder and decoder weights, approximately 10 M parameters, rather than dense high-resolution voxel outputs or large explicit meshes. Third, the system is trained end-to-end from raw volumes to surface reconstructions without hand-crafted geometric priors [2509.12068].

The limitations are equally explicit. Inference speed depends on the number of sampled grid points, so very high-resolution grids such as $1024^3$ incur non-trivial compute. The model does not provide explicit topology control, and rare topological errors may occur when organs touch. The method also depends on careful surface-near sampling; the paper notes that uniform sampling alone may under-represent thin structures.

Several extensions are proposed in the paper. These include replacing occupancy with signed distance functions for improved gradient signal near surfaces, incorporating geometric regularizers such as curvature smoothness, using multi-resolution hashing or neural-radiance-field-style accelerations to speed inference, and extending the formulation to temporal volumes for motion-compensated organ modeling in dynamic CT or MRI. These directions indicate that ImplMORe is not only a reconstruction model but also a framework for continuous-shape learning from medical volumes, with direct relevance to high-fidelity surface reconstruction, morphometric analysis, and surgical planning.

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