PaperlayerView exact revision on arXiv

Source-linked AI summary

Bound-Conditioned Latent Inference for Progressive Image Compression

Jaeseok Jang, Seungmin Jeon, Kwang Pyo Choi, Chang-Su Kim

arXiv:2610.30966v1eess.IVcs.CV

TL;DR

Progressive compression must infer unresolved latents from partial observations in a decodable bitstream prefix, while existing trit-plane codecs leave the induced interval constraints underused. BLI jointly refines entropy-model parameters and latent estimates under shrinking bounds. It achieves state-of-the-art rate-distortion performance among progressive codecs, with reported Kodak BD-rate reductions over DPICT and CTC.

  • Problem

    Existing trit-plane codecs mainly treat decoded trits as discrete symbols and do not explicitly use their induced feasible intervals for continuous latent inference.

    Source: §1 · p. 2

  • Method

    BLI uses decoded-trit bounds and shared hyperprior information to jointly refine Gaussian entropy-model parameters and latent estimates as intervals shrink.

    Source: §1 · p. 2

  • Results

    17.78% over DPICT and 7.96% over CTC on Kodak: BLI achieves state-of-the-art rate-distortion performance among progressive codecs.

    Source: §1 · p. 3

  • Takeaways & Limitations

    BLI replaces CTC’s plane-specific prediction networks with a shared model that uses about 5.3× fewer parameters and achieves lower latency.

    Source: §1 · p. 3, §4.1 · p. 8

    The evaluation uses Lee et al.’s R-D-prioritized transmission order; designing orders better matched to BLI remains future work.

    Source: §4.3 · p. 10

Abstract

from arXiv · show

Progressive image compression reconstructs images from prefixes of a single bitstream and therefore involves sequential latent inference under partial observations. Existing trit-plane codecs mainly treat decoded trits as discrete symbols for probability prediction, without fully exploiting their role as interval constraints on the underlying continuous latents. We propose bound-conditioned latent inference (BLI), a framework that reformulates progressive trit-plane coding as sequential latent inference under shrinking interval constraints. At each coding step, the trits decoded so far define lower and upper bounds for each latent element. BLI uses the center and width of these bounds, together with hyperprior information shared by the encoder and decoder, to jointly refine the Gaussian parameters $(\mu,\sigma)$ for entropy modeling and the latent estimate $\hat{y}$ for reconstruction. As additional trits are decoded, the feasible intervals shrink monotonically, yielding tighter constraints for the next inference step and enabling flexible in-plane refinement schedules. Experiments on Kodak, CLIC, and JPEG-AI show that BLI achieves state-of-the-art rate-distortion performance among progressive image codecs, reducing BD-rate by $17.78\%$ over DPICT and by $7.96\%$ over CTC on Kodak, while replacing CTC's plane-specific predictors with a shared model that uses about $5.3\times$ fewer parameters and achieves lower latency than CTC.

1 Introduction

BLI treats progressive trit-plane coding as inference over continuous latents constrained by decoded trits, rather than only as discrete-symbol prediction. It jointly refines entropy-model parameters and reconstructions, supporting flexible refinement schedules and strong progressive-codec results.

1 Introduction

  • Progressive decoding supports image reconstruction from bitstream prefixes, serving adaptive streaming, bandwidth-limited transmission, and multi-quality storage.Source: §1 · p. 1
  • At a fixed trit-plane level, BLI can encode the plane in one, two, or four substeps, allowing more frequent bound-conditioned updates.Figure 1 contrasts the schedules while holding the quantization level constant.Source: Figure 1 · p. 2, §1 · p. 2
  • Existing trit-plane codecs mainly use decoded trits as discrete symbols and do not explicitly infer continuous latents within the feasible intervals those trits define.Source: §1 · p. 2
  • BLI recasts trit-plane coding as sequential inference under shrinking interval constraints, with decoded trits setting bounds on each continuous latent element.Source: §1 · p. 2
  • Using interval centers and widths plus shared hyperprior information, BLI jointly refines Gaussian entropy-model parameters and latent estimates for reconstruction.Source: §1 · p. 2
  • 17.78% over DPICT and 7.96% over CTC on Kodak: BLI achieves state-of-the-art rate-distortion performance among progressive codecs.Source: §1 · p. 3

2 Related Work

Related work spans learned fixed-rate codecs, entropy models that exploit latent dependencies, and scalable or progressive coding. Earlier progressive trit-plane methods model decoded trits primarily as discrete symbols, leaving their interval constraints unused for continuous latent inference.

2 Related Work

  • Learned codecs replace hand-crafted transforms and entropy models with neural networks, while hyperpriors transmit side information about latent distributions to improve entropy estimation.Source: §2 · p. 3
  • Autoregressive context models improve compression through sequential latent prediction but incur high coding latency; partially parallel models reduce that cost by exploiting latent correlations.Source: §2 · p. 3
  • Transformer-based codecs and entropy models improve global context or long-range dependency modeling, but most are not designed for a single progressively decodable bitstream.Source: §2 · p. 3
  • Variable-rate methods can control rates from one model, but generally require separately encoded bitstreams, unlike progressive codecs whose prefixes are decodable at multiple quality levels.Source: §2 · p. 3
  • PLONQ uses nested quantization, while DPICT and CTC use trit-plane coding; DPICT and CTC primarily treat decoded trits as discrete symbols rather than interval constraints for continuous inference.Source: §2 · p. 3

3 Proposed Algorithm

BLI recasts progressive trit-plane coding as sequential inference over feasible latent intervals, refining entropy-model parameters and reconstructions as decoded trits tighten those intervals. Its codec uses bound-conditioned features and a modified FTIC implementation with flexible transmission schedules.

3 Proposed Algorithm

  • BLI jointly refines Gaussian entropy-model parameters and latent estimates within trit-defined bounds as those bounds shrink during progressive decoding.Unlike discrete context prediction, it performs bound-conditioned inference at each refinement step.Source: §3 · pp. 3–4, Figure 2 · p. 4

3.1 Bound-Conditioned Latent Inference

  • At each coding step, decoded trits determine interval constraints, while BLI uses interval centers and widths with hyperprior parameters to estimate the next Gaussian parameters and reconstruction.The Gaussian parameters encode the next trit subset; the latent estimate is consistent with the bounds available before that subset is coded.Source: §3.1 · p. 4

3.2 BLI Codec Architecture

  • A stack of Swin attention blocks models spatial dependencies in partially decoded latents, and CNN blocks with plane-wise MLP heads predict Gaussian parameters and latent estimates.The interval center and half-width are concatenated with CNN features, and output rescaling keeps estimates within the feasible interval.Source: §3.2 · p. 5, Figure 4 · p. 6

3.3 Implementation

  • The implementation replaces FTIC’s channel-wise autoregressive entropy model with a non-autoregressive hyperprior that initializes Gaussian parameters from the hyperlatent tensor.Training uses random trit assignments across four steps per plane; evaluation uses R-D-prioritized transmission and more finely subdivides planes closer to the LST.Source: §3.3 · p. 6
  • BLI is optimized in two stages, first training the modified FTIC backbone and then optimizing BLI with endpoint rate and distortion losses.The second stage uses λ = 0.0483 and runs for 0.5M iterations at a learning rate of 5 × 10^-5.Source: §3.3 · p. 6

4 Experimental Results

BLI outperforms progressive-codec baselines across the reported datasets and bitrate ranges, while using a shared model with fewer parameters than FTIC-CTC and lower latency. Ablations show gains from bound-aware design and more frequent in-plane refinement; the evaluation uses an R-D-prioritized transmission order.

4.1 Comparative Assessment

  • 17.78%, 17.12%, and 17.52%: BLI reduces PSNR BD-rate relative to FTIC-DPICT on Kodak, CLIC, and JPEG-AI, respectively.Table 1 reports PSNR BD-rates relative to FTIC-DPICT.Source: Table 1 · p. 7, §4.1 · p. 8
  • BLI uses about 5.3× fewer parameters than FTIC-CTC and has the lowest latency among the compared codecs.The shared BLI module replaces plane-specific predictors; the latency reduction is attributed to efficient Gaussian interval integration.Source: Table 2 · p. 7, §4.1 · p. 8
  • BLI achieves the best R-D performance among progressive codecs over most bitrates, remains competitive with fixed-rate learned codecs, and surpasses STF over most of the MS-SSIM range.Fixed-rate baselines are optimized separately for each target rate, whereas BLI generates all R-D points from one progressive codec.Source: §4.1 · p. 7
  • At nearly identical bitrates, BLI better preserves high-frequency details and produces fewer noticeable artifacts than the compared codecs.The qualitative comparison reports blur around petal boundaries and feather textures for other codecs.Source: Figure 6 · p. 8, §4.1 · p. 8

4.2 Analysis

  • Removing bound-width input and interval-rescaled constraints, removing the reconstruction branch, or reducing module capacity worsens the reported BD-rate results.The variants yield −15.64%, −15.01%, and −12.48%, respectively.Source: Table 3 · p. 9, §4.2 · p. 9
  • On Kodak, BD-rate improves as refinement steps per trit-plane increase: −10.40% for one step, −12.90% for two, −14.79% for four, and −17.78% for the full schedule.The full schedule uses K_end = {4, 8, 14, 30, 54}.Source: §4.2 · pp. 9–10, Table 3 · p. 9, Figure 9 · p. 9
  • BLI achieves −19.87% versus CTC's −14.84% on the Cheng et al. backbone, and improves BD-rate from −6.86% to −22.30% on the Liu et al. backbone; it also beats discrete prediction at both tested schedules.The discrete-prediction comparisons are −10.40% vs. −9.30% for one step and −17.78% vs. −14.06% for the full schedule.Source: §4.2 · p. 10, Table 4 · p. 10, Table 5 · p. 10

4.3 Limitations and Future Work

  • The evaluation adopts Lee et al.'s R-D-prioritized transmission order; orders better matched to BLI and the remaining gap to recent fixed-rate codecs are future-work directions.The paper notes that the fixed-rate performance gap is expected for progressive codecs that reconstruct from bitstream prefixes.Source: §4.3 · p. 10

5 Conclusions

BLI reframes trit-plane coding as sequential inference over shrinking latent intervals and jointly refines entropy-model parameters and reconstruction estimates. Experiments report state-of-the-art rate-distortion performance among progressive codecs, with fewer parameters and lower latency than CTC.

5 Conclusions

  • BLI reformulates trit-plane coding as sequential latent inference under shrinking interval constraints.The bounds are updated as trits are decoded, and BLI jointly refines Gaussian parameters for entropy modeling and latent estimates for reconstruction.Source: §5 · p. 10
  • BLI achieves state-of-the-art rate-distortion performance among progressive codecs and preserves high-frequency details more faithfully.The conclusion attributes refinement to progressively updated bounds and flexible in-plane autoregressive updates.Source: §5 · p. 10
  • BLI replaces CTC's plane-specific predictors with a shared module that uses fewer parameters and achieves lower latency.Source: §5 · p. 10

A Additional Experimental Results

The appendix provides additional rate-distortion comparisons for Kodak, CLIC 2021, and JPEG-AI. Figure 10 shows PSNR and MS-SSIM curves, while Table 6 summarizes BD-rates relative to FTIC-DPICT.

A Additional Experimental Results

B.1 Architecture Configurations

The BLI framework is embedded in FTIC with 128 hyper-latent channels and 320 primary-latent channels. Its architecture uses paired initial-distribution predictors and a 10-layer Swin-attention BLI model.

B.1 Architecture Configurations

  • BLI is embedded in FTIC with 128 channels for hyper latent Z and 320 for primary latent Y.The latent-related tensors have 320 channels and spatial dimensions one-sixteenth of the input image resolution.Source: §B.1 · pp. 13–14
  • Two identical predictor networks estimate the initial Gaussian parameters.Each predictor uses a residual CNN block, two FAT blocks, and a final convolution layer to produce a 320-channel output.Source: §B.1 · p. 14
  • The BLI architecture uses 10 Swin-attention layers with hidden dimension 960, 16 attention heads, and window size 8.Each CNN branch uses four depthwise convolution layers.Source: §B.1 · p. 14

B.2 Training Loss

BLI training and evaluation divide each trit-plane into coding steps, progressively update latent bounds, and use a nonuniform evaluation schedule that allocates more steps to lower-significance planes.

B.2 Training Loss

  • The training loss weights plane endpoints by inverse squared quantization interval, decreasing weights by a factor of 1/9 from the LST to the MST.The endpoint indices are {4, 8, 12, 16, 20}.Source: §B.2 · p. 14

B.3 Transmission Schedule

  • Training uniformly divides each trit-plane into four steps, first randomizing trit assignments before fine-tuning with the evaluation transmission order.The training endpoints are {4, 8, 12, 16, 20}.Source: §B.3 · p. 14
  • Evaluation uses step endpoints {4, 8, 14, 30, 54}, allocating more refinement steps to planes nearer the LST.Within each plane, trits are ordered by descending predicted distortion reduction per bit, −∆D/∆R.Source: §B.3 · p. 14

B.4 Trit Partitioning Within a Trit-Plane

  • The number of trits required for each latent element is derived from the width of a symmetric Gaussian interval containing probability mass 1 − 10^-9.The interval width is 2κΣ0_i, and the count is the ceiling of its base-3 logarithm; elements with enough trits are partitioned into coding-step subsets.Source: §B.4 · pp. 14–15

B.5 Algorithmic Workflow

  • Each step’s decoded trits shrink the corresponding latent bounds; training obtains those bounds directly from the ground-truth latent rather than entropy decoding.The encoder and decoder share the transmission schedule to identify which trits belong to each step.Source: §B.5 · p. 15

B.6 Baseline Implementations

The baseline implementations combine released or official codec implementations with specified preprocessing and encoding settings for traditional codecs.

B.6 Baseline Implementations

  • For FTIC-based progressive baselines and BLI, the original entropy model is replaced with the described structure and training starts from pretrained FTIC weights.The pretrained weights are from FTIC’s official GitHub repository.Source: §B.6 · pp. 15–16
  • JPEG2000 uses the open-source implementation, with RGB images converted to raw format before processing.The specified encoder rate range is {15:150}.Source: §B.6 · p. 16
  • BPG444 uses Bellard’s software with 4:4:4 chroma format and x265 encoding.The listed quality range is {26:52}.Source: §B.6 · p. 16
  • VTM 12.0 is run with 8-bit input and RGB-to-GBR conversion for encoding, followed by GBR-to-RGB conversion for decoding.For other comparison methods, the study uses official implementations or reported results from their papers.Source: §B.6 · p. 16

C.1 Computational Complexity

BLI’s repeated in-plane inference increases neural computation, while lower non-neural processing overhead yields the lowest end-to-end latency among the compared progressive codecs. Transmission ordering mainly affects intermediate-prefix efficiency, and entropy refinement contributes more to rate-distortion gains than latent reconstruction.

C.1 Computational Complexity

  • BLI achieves the lowest end-to-end latency among the three progressive codecs because direct Gaussian interval integration reduces non-neural processing overhead.Its in-plane autoregressive refinement requires more neural computation than FTIC-DPICT, while its FLOP count is comparable to FTIC-CTC.Source: §C.1 · pp. 16–17, Table 7 · p. 17

C.2 Sensitivity to Transmission Ordering

  • Transmission ordering substantially affects full progressive rate-distortion performance but has relatively little effect at fully decoded trit-plane endpoints.The R-D-prioritized order sends trits expected to yield larger distortion reduction per bit earlier within each plane.Source: §C.2 · p. 17, Table 8 · p. 17

C.3 Entropy Modeling vs. Latent Reconstruction

  • Disabling entropy refinement reduces the BD-rate gain to −10.24%, while replacing explicit latent prediction with the Gaussian expectation changes it from −17.78% to −16.38%.The reported ablation indicates a larger contribution from entropy refinement, with a smaller but consistent additional gain from latent reconstruction.Source: §C.3 · p. 17, Table 9 · p. 18

C.4 Perceptual Evaluation

On Kodak at low bitrates, BLI improves both perceptual metrics reported, and reconstructed-image examples extend across Kodak, CLIC, and JPEG-AI. Separate examples probe challenging color patterns on Tecnick.

C.4 Perceptual Evaluation

  • BLI achieves the lowest LPIPS and DISTS values at 0.10, 0.15, and 0.20 bpp among the evaluated codecs.The comparisons cover conventional codecs and progressive learned baselines on Kodak.Source: §C.4 · p. 18

C.5 Reconstructed Images

  • Progressive reconstructions from the PSNR-trained BLI model are shown for Kodak, CLIC, and JPEG-AI images.Bitrate, PSNR, and MS-SSIM are reported below the Kodak images shown in Figures 11–13.Source: §C.5 · p. 18, Figure 11 · p. 19, Figure 12 · p. 20

C.6 Tests on Challenging Color Patterns

  • Tecnick examples test BLI on smooth low-frequency gradients and sharp chromatic edges.Figure 20 presents two images for this challenging-color-pattern evaluation.Source: §C.6 · p. 18, Figure 20 · p. 28

Related papers

Loading 2610.30966v1…