Practical Lossless Volumetric Medical Image Compression via Tri-plane Context Tree Learning

Yuanchao Bai; Yifan Zhao; Kai Wang; Yuanbo Du; Jie Cheng; Teng Fang; Xianming Liu; Wen Gao

eess.IVAug 14, 2026

Practical Lossless Volumetric Medical Image Compression via Tri-plane Context Tree Learning

Authors: Yuanchao Bai, Yifan Zhao, Kai Wang, Yuanbo Du, Jie Cheng, Teng Fang, Xianming Liu, Wen Gao

Organizations: Faculty of Computing, Harbin Institute of Technology, Harbin, 150001, China · Huawei Tech. Company, Ltd. · School of Electronics Engineering and Computer Science, Peking University, Beijing, 100871, China, and Pengcheng Laboratory, Shenzhen, 518055, China

Abstract

Lossless compression of volumetric medical images is of paramount importance for clinical and research applications where data fidelity is essential. Traditional compression methods are often limited in efficiency due to rigid, handcrafted models. Conversely, deep neural network (DNN)-based compression methods, while effective, demand substantial computational resources, hindering deployment in resource-constrained settings. To address these challenges, we propose a novel tri-plane context tree (TCT)-based method for lossless volumetric medical image compression that delivers high performance without relying on DNNs or external training data. To exploit intra-slice and inter-slice redundancies, we introduce a compact tri-plane context representation that decomposes complex 3D context modeling into efficient 2D modeling on three orthogonal planes. By integrating this representation with a context tree framework, we develop an input-specific TCT model employing an adaptive binary tree structure. At each tree node, the model dynamically selects from a suite of tri-plane based predictors and contextual feature extractors, enabling data-adaptive context modeling tailored to local structural characteristics. Instead of offline training, we sample a subset of the input volume to learn the TCT model by optimizing the minimum description length (MDL) through iterative construction and pruning. With the learned TCT model, each pixel retrieves its corresponding context, computes the prediction residual using the predictor dictated by the context, and performs entropy encoding based on the associated histograms. Experimental results demonstrate that the proposed method achieves compression performance on par with recent DNN-based methods on multiple datasets, while maintaining low computational cost and fast coding speeds, making it highly applicable in practice.

Figures & tables

Notation	Description
${\mathbf{I}}$	volumetric medical image
${\mathbf{I}}_{idx}$	pixel set at index $idx\in\{<i,{\mathcal{S}},{\mathcal{P}},\ldots\}$
$I_{idx}$	pixel at index $idx\in\{i,L[0],L[1],\ldots\}$
${\mathbf{C}}$ , $C_{j}$	context set ${\mathbf{C}}=\{C_{1},\ldots,C_{M}\}$ , context $C_{j}\in{\mathbf{C}}$
${\mathrm{pred}}$ , ${\mathrm{pred}}_{j}$	predictor and predictor assigned to $C_{j}$
${\mathbf{r}}_{idx}$	residual set at index $idx$

TABLE I: Notations for TCT model and TCT-based compression method.

Fig. 1: Example of a volumetric medical image and its tri-plane representation, including x-y, y-z, x-z planes.

Panel of Figure 3 — Fig. 2: Illustration of tri-plane context representation for encoding pixel $I_{i}$ . (a) all previously encoded pixels ${\mathbf{I}}_{<i}$ . (b) x-y context plane. (c) y-z context plane. (c) x-z context plane. Red: the pixel $I_{i}$ . Blue: the previously encoded pixels. Orange: the pixels in each context plane.

Fig. 3: Diagram of the tri-plane context tree (TCT) model. Each internal node is assigned a feature index $k$ corresponding to the $k$ -th feature $f^{k}_{i}$ ’s, which are derived from a combination of pixels (marked with orange) residing on the three context planes. The internal node is also associated with a threshold $t$ for binary partitioning. Each leaf node represents a distinct context. For each pixel, the TCT model is traversed from the root to the leaf based on the pixel’s features, retrieving the corresponding context.

Fig. 4: Block diagram of the TCT-based volumetric medical image compression. The TCT-based compression method requires no offline training. Instead, it learns a customized, input-specific context model ${\mathcal{T}}$ by performing TCT learning on a sample set ${\mathcal{S}}$ of the input 3D volume. During compression, each pixel retrieves its corresponding context from the learned model ${\mathcal{T}}$ to enable adaptive prediction and entropy coding. Finally, both the learned TCT model and the compressed image data are stored into the bitstream to ensure decodablity.

Fig. 5: Labeling of neighboring pixels used in prediction and contextual feature extraction on three context planes. The x-y, y-z and x-z context planes enjoy the same context pattern. The $\bigtriangleup$ denotes the current pixel. The $L$ denotes the left pixel of $\bigtriangleup$ . The $LL$ denotes the left-left pixel of $\bigtriangleup$ . The $T$ denotes the top pixel of $\bigtriangleup$ . The $TT$ denotes the top-top pixel of $\bigtriangleup$ . The $LT$ denotes the left-top pixel of $\bigtriangleup$ . The $LLT$ denotes the left-left-top pixel of $\bigtriangleup$ . The $RT$ denotes the right-top pixel of $\bigtriangleup$ .

Predictor	Sub-predictor
Median-2D	${\mathrm{median}}(I_{L[0]},I_{L[0]}+I_{T[0]}-I_{LT[0]},I_{T[0]})$
Median-3D	${\mathrm{median}}(I_{L[0]},I_{L[0]}+I_{T[0]}-I_{LT[0]},I_{T[0]})$
	${\mathrm{median}}(I_{L[1]},I_{L[1]}+I_{T[1]}-I_{LT[1]},I_{T[1]})$
	${\mathrm{median}}(I_{L[2]},I_{L[2]}+I_{T[2]}-I_{LT[2]},I_{T[2]})$
Blending-3D	$I_{L[0]}-I_{T[0]}+I_{RT[0]}$
	$I_{L[0]}+I_{T[0]}-I_{LT[0]}$

TABLE II: Tri-plane based predictors and the corresponding sub-predictors

Fig. 6: Quadruple representation $(zbit,sbit,msb,lsb)$ of prediction residual.

Type	Feature Value
Gradient-2D	$I_{L[0]}-I_{LT[0]}$
	$I_{LT[0]}-I_{T[0]}$
	$I_{T[0]}-I_{RT[0]}$
	$I_{T[0]}-I_{TT[0]}$
	$I_{L[0]}-I_{LL[0]}$
	$I_{LL[0]}+I_{LT[0]}-I_{LLT[0]}-I_{L[0]}$

TABLE III: Tri-plane based features and the corresponding values

Fig. 7: Illustration of the proposed two-step TCT learning algorithm.

	Chaos	MosMedData	Trabit	MRNet
Type	Abdomen CT	Lung CT	Brain MRI	Knee MRI
Training Set †	20	125	70	1130
Test Set	20	45	30	120
Bit Depth	16	16	16	8
Slice Count	78 $\sim$ 294	32 $\sim$ 72	176	17 $\sim$ 61
Resolution	512 $\times$ 512	512 $\times$ 512	176 $\times$ 208	256 $\times$ 256

TABLE IV: Overview of volumetric medical image datasets in experiments. † Training sets are for DNN-based methods.

Codec	Chaos		MosMedData		Trabit		MRNet
Codec	BPP $\downarrow$	Compression Ratio $\uparrow$	BPP $\downarrow$	Compression Ratio $\uparrow$	BPP $\downarrow$	Compression Ratio $\uparrow$	BPP $\downarrow$	Compression Ratio $\uparrow$
Traditional
PNG	7.09	2.256	7.09	2.257	3.08	5.190	4.56	1.755
JPEG-LS [ 51 ]	5.08	3.148	5.02	3.188	2.22	7.194	4.06	1.971
CALIC [ 54 ]	-	-	-	-	-	-	3.93	2.036
JPEG2000 [ 42 ]	5.05	3.169	5.32	3.009	2.58	6.204	4.17	1.920

TABLE V: Lossless image compression performance of our TCT-based volumetric medical image compression method, compared with other lossless compression methods on Chaos, MosMedData, Trabit and MRNet datasets. The best performance is marked in bold , the second-best is marked with an underline , and the third-best is marked with a double-underline . † Using the released CT compression model trained on MosMedData dataset.

Codec	GPU Max Usage	Chaos		MosMedData
Codec		Enc.T.	Dec.T.	Enc.T.	Dec.T.
Traditional (CPU)
JPEG-LS	-	0.02s	0.02s	0.03s	0.03s
JPEG-XL	-	2.18s	0.05s	4.08s	0.07s
JP3D	-	0.04s	0.04s	0.07s	0.07s
HEVC-RExt	-	4.01s	0.02s	5.61s	0.03s

TABLE VI: Average coding time per slice of volumetric medical image compression methods. The DNN-based methods run on GPU with maximum GPU usage reported.

M-2D	M-3D	B-3D	Chaos	MosMedData	Trabit	MRNet
$\checkmark$	$\times$	$\times$	4.64	4.72	2.00	3.83
$\checkmark$	$\checkmark$	$\times$	4.44	4.71	1.97	3.83
$\checkmark$	$\checkmark$	$\checkmark$	4.27	4.64	1.91	3.79

TABLE VII: Effects of Predictors on the compression performance. M-2D, M-3D, B-3D denote Median-2D, Median-3D and Blending-3D.

Panel of Figure 15 — Fig. 8: The percentage of predictor and feature selections in our TCT-based compression method on the Chaos dataset. (a) predictor selection. (b) feature selection. The M-2D, M-3D and B-3D denote the Median-2D, Median-3D and Blending-3D respectively.

Panel of Figure 16 — Fig. 9: Visualization of the predictor selection map generated by our TCT-based compression method for a 2D slice of a 3D CT scan. (a) 16-bit CT slice mapped to 8-bit for visualization. (b) predictor selection map. Red: Median-2D. Yellow: Median-3D. Blue: Blending-3D.

G-2D	G-3D	Pred	Chaos	MosMedData	Trabit	MRNet
$\checkmark$	$\times$	$\times$	4.36	4.67	1.93	3.86
$\checkmark$	$\checkmark$	$\times$	4.30	4.66	1.93	3.85
$\checkmark$	$\checkmark$	$\checkmark$	4.27	4.64	1.91	3.79

TABLE VIII: Effects of features on compression performance. G-2D, G-3D, Pred denote Gradient-2D, Gradient-3D and Prediction.

Percentage	Chaos	MosMedData	Trabit	MRNet
Model	0.04%	0.08%	0.11%	0.14%
Image Data	99.96%	99.92%	99.89%	99.86%

TABLE IX: Average proportions of TCT model and compressed image data.

TCT Pruning	Histogram Num.		Comp. Performance
TCT Pruning	$\times$	$\checkmark$	$\times$	$\checkmark$
Chaos	4048	224	4.28	4.27
MosMedData	2552	198	4.67	4.64
Trabit	691	106	1.93	1.91
MRNet	587	111	3.82	3.79

TABLE X: Effects of TCT pruning on average number of histograms and compression performance.

Fig. 10: Effects of $(\lambda,u)$ on average lossless compression performance (bpp) on random samples from Chaos, MosMedData, Trabit and MRNet datasets. The (50, 224) is selected for all four datasets.

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