MoRIC: A Modular Region-based Implicit Codec for Image Compression
Authors: Gen Li
Haotian Wu
Deniz Gunduz
Venue: NeurIPS 2025 poster ()
Keywords: Implicit neural representation
source coding
overfitted image compression
low-complexity image codec
layered compression.
Primary area: applications

Abstract: We introduce Modular Region-Based Implicit Codec (MoRIC), a novel image compression algorithm that relies on implicit neural representations (INRs). Unlike previous INR-based codecs that model the entire image with a single neural network, MoRIC assigns dedicated models to distinct regions in the image, each tailored to its local distribution. This region-wise design enhances adaptation to local statistics and enables flexible, single-object compression with fine-grained rate-distortion (RD) control. MoRIC allows regions of arbitrary shapes, and provides the contour information for each region as separate information. In particular, it incorporates adaptive chain coding for lossy and lossless contour compression, and a shared global modulator that injects multi-scale global context into local overfitting processes in a coarse-to-fine manner. MoRIC achieves state-of-the-art performance in single-object compression with significantly lower decoding complexity than existing learned neural codecs, which results in a highly efficient compression approach for fixed-background scenarios, e.g., for surveillance cameras. It also sets a new benchmark among overfitted codecs for standard image compression. Additionally, MoRIC naturally supports semantically meaningful layered compression through selective region refinement, paving the way for scalable and flexible INR-based codecs.

MoRIC: A Modular Region-based Implicit Codec for Image Compression
Gen Li;
Haotian Wu"! Deniz Gündüz
Department of Electrical and Electronic Engineering Imperial College London, London SW7 2AZ, U.K.
{gen. 1i22, haotian. wu17, d. g.guuduzz@@iperiiaa ac. https//reddaiivvaaiihhhhhMMMBR
Abstract
We introduce Modular Pegion-Based Implicit Codec (MoRIC), novel image compression algorithm that relies on implicit neural representations (INRs). Un- like previous INR-based codecs that model the entire image with single neural network, MoRIC assigns dedicated models to distinct regions in the image, each tai- lored its local distribution. This region-wise design enhances adaptation local statistics and enables flexible, single-object compression with fine-grained rate- distortion (RD) control. MoRIC allows regions of arbitrary shapes, and provides the contour information for each region as separate information. In particular, it in- corporates adaptive chain coding for lossy and lossless contour compression, and a shared global modulator that injects multi-scale global context into local overfitting processes in a coarse-to to-fiee manner. MoRIC achieves sate-of-the-an performance in single-object compression with significantly lower decoding complexity than existing learned neural codecs, which results in highly efficient compression approach for fixe-bbckground scenarios, e.g., for surveillance cameras. It also sets new benchmark among overfitted codecs standard image compression. Additionally, MoRIC naturally supports semantically meaningful layered compres- sion through selective region refinement, paving the way for scalable and flexible INR-based codecs.
Introduction
Traditional image and video codecs 5 515,8 9 rely on hand-crafted transforms to capture statistical correlations in the data, and exploit redundancies rooted in human perception for compression. Recently, deep learning-basse codecs have demonstrated remarkable rate-distortion (RD) performance by replacing manually designed analysis and synthesis transforms with neural networks 15) 22
However, this advancement comes with significantly increased model complexity and decoding cost that often far exceed those of commercial codees, limiting their practicality in real-world applications [26] [4). Furthermore, these neural approaches typically require large-scale training or advanced models 47 to generalize across diverse data distributions. Consequently, developing codecs that balance low computational complexity and high performance remains critical open challenge [58].
To address these limitations, overfitted codecs have emerged, leveraging implicit neural representa- tions (INRs) [50) compress each image individually with low decoding complexity. INRs employ lightweight lulti-layer perceptrons (MIPss) parameterize continuous functions
48 37 with the
quantized network weights serving as a compact, signal-specific compressor
First INR-based
'These authors contributed equally to this work and are listed alphabetically. Corresponding author: Haotian Wu (haotian. wull w @imperial.ac.uk)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Modular Region-based Implicit Codec
Object-aware compression
C' coding
Reglon-wise compression
partition
Lovil EERAA
LOV
coding
networe
svertting
Shored Ghobel Mouudattrr
Mage
Scalable layored compression
Layer-1
Layer-
Rofiee
Figure 1: Illustration of the proposed framework, highlighting its key features: precise single-object compression, region-wise adaptive coding, and scalable layered compression. MoRIC enables fine- grained control over regions and objects for overfitted codecs, improving RD performance through region-wise fitting and global-local modulation. It also introduces layered compression, supporting semantically meaningful coarse reconstructions to be progressively refined with additional bits.
image codec, COIN, was introduced in [16]. was later followed by the COMBINER series [2] 23 the COOL-CHIC series 330 31). and the C3 series [27] which have gradually improved the RD performance and perceptual quality. Notably, these approaches now surpass classical codecs such as BPG 5 and HEVC (51) while maintaining low decoding complexity.
Despite these advances, overfitted codecs still lag behind classical and neural codecs like VTM [0] and MLIC+ [25] 26 in RD performance. Achieving higher fidelity often demands more complex networks, which, in turn, increases the bitrate. Architectural innovations for INRs in the context of data compression remain underexplored, with most overfitted codecs employing fixed architectures across diverse images, limiting both performance and adaptability. In practice, images exhibit varying statistical characteristics and compression difficulty, image. These limitations underscore the need for a new overfitted codec framework that improves performance while enabling flexibility and modularity.
across different regions within the same
Unlike previous codecs that overfit single neural network to the entire image, we propose "divide and conquer" approach, called MoRIC. MoRIC first partitions the image into distinct regions, and overfits a separate local synthesis network (LSN) to each region. This allows specialization to local distributions, and improves compression efficiency by reducing the complexity of individual LSNs. Unlike transform- based codecs, INRs are not limited to fixed rectangular shapes, and can be trained for regions of arbitrary shapes. However, for reconstruction of the whole image, need to transmit the contour information each region (except the background) separately. We note that a single INR trained for the whole image implicitly learns not only the statistical characteristics of all the image regions, but also the contour information. We, instead, employ a dedicated efficient contour coding scheme called C*. MoRIC further employs shared global modulator that injects global context to mitigate artifacts from local-only overfitting. Together, these components enable fine-grained control of the RD trade-off and introduce greater fiexibility and representational capacity to the codec.
Our design is motivated by three key findings: (1) Fine-grained and flexible region-based overfitting improves RD performance and adaptability. (2) Chain coding enables efficient contour compression (lossy and lossless), and supports modular INRs with faster convergence via cross-region modulation. (3) Semantic generalization emerges from combining global modulation with local overfitting, allowing flexible layered compression with semantic-awe aware synthesis beyond pixel-level fidelity.
MoRIC enables modular region-ber based compression with low decoding complexity, achieving state- of-the-arl performance among overfitted codecs across diverse scenarios. It accurately overfits target regions while reducing contour overhead, outperforming the leading neural codee *

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with decoding complexity below 800 MACs/pixel on single-object compression tasks. Its multiscale and coarse-to-inee modulation enhances reconstruction quality and streamlines coding through dynamic selection of regions requiring finer detail, enabling fine-grained complexity control and faster training. As a result, MoRIC establishes new benchmarks for overfitted codecs, surpassing VTM in standard image compression tasks. Moreover, MoRIC is the first overfitted codec to support layered compression, enabling semantic-aware, progressive reconstruction across regions. This design balances distortion, computation, and compression cost, paving the way for future research on scalable, flexible overfitted codecs. Our main contributions are:
We propose MoRIC, modular region-based implicit codec that overfits images region by re- gion. This region-wise compression design improves adaptation to local content distributions and supports flexible, region-specific control for enhanced compression efficiency.
We introduce adaptive chain coding, named C* coding, for efficient lossy and lossless contour coding, combined with shared modulation in a coarse-to-fing fashion, enabling MoRIC achieve state-of-the-ar single-object compression with significantly reduced decoding complexity. Notably, the open-sourced C* coding can be of independent interest for broader INR-based research beyond compression.
Leveraging region- based compression, enhanced by C* coding and a global-loca modulation mechanism, MoRIC sets up new baselines among overfitted codecs for standard full image compression task while enabling fine-grained RD control and region-specific adaptation.
Moreover, MoRIC reveals that region--pecific codees can generalize across regions, enabling semantically meaningful reconstructions. Its layered, coarse-to-fine finf design allows local codees to infer and progressively refine other regions, with additional models selectively transmitted to enhance fidelity, supporting scalable, flexible layered compression.
2 Related work
2.1 Overfitted codec
Overfitting a parametric function to single image offers low-complexity alternative to standard
neural codecs. COIN [16] pioneered this by training lightweight INR map pixel coordinates to
RGB values, with quantized parameters forming the bitstream. Later works [45] 46 17] employed
meta-learning for improved generalization. However, the COIN series still lagged behind standard
autoencoder (AE) based codecs in RD performance. To address this, the COMBINER series [2T] 23
introduces variational INRs and leverages relative entropy coding for RD-optimized compression.
The COOL-CHIC series 30 further enhances RD performance by incorporating learnable la- tent and entropy models. Its extensions, including COOL-CHICV2 [31. C3 27 and COOL- CHICv3/v4 322, introduce significant architectural advances such as soft-rounding, Kumaraswamy noise, conditional entropy coding, and Wasserstein distortion. These innovations enable performance that surpasses classical codees like BPG [5] and HEVC (51] More recently. LotteryCodec (56) is proposed to encode image statistics into the random network substructure for flexible complexity and better performance. Despite this progress, current overfitted codecs still fall short of advanced codecs like VTM [10] or + (25) in RD performance. Moreover, they lack support for diverse needs such as layered compression or fine- -reeggr regional control. These limitations motivate our development of a more sophisticated, low-cost overfitted codec with flexible coding strategies.
2.2 Region partitioning for INRs
By modeling signals as continuous functions, INRs offer expressive representations for various tasks such as view synthesis, image inpainting, and super-resolution [50]
37 13. Partitioning
the input space into local regions has proven effective in improving detail fidelity for INR- based models 24, (53. Chabra et al. [II] introduced local latent vectors per partition, later extended by Mehta et al. [36] using a modulator network. Follow-up work explored multi-resolution partitioning
14 55 and hierarchical tree structures for parameter sharing (57). Input region partitioning can also accelerate training for faster convergence by enabling coarse-to-fine modeling 43), semantic segmentation (35), and input decoupling (34. Ashkenazi et al. I proposed croppable INRs that support editability without retraining and fine- finengriied downstream control.

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Although shape-based based image/video coding has received significant research interest in the past 44] has not found applications in practice. In transform-based coding, this requires designing specific transforms [49 33 for arbitrary shapes, which creates significant complexity. On the other hand, INRs are particularly appropriate for this as they can trained on arbitrary shapes.
3 Methodology
3.1 Preliminary
Standard overfitted codec. At its core, overfitted codec compresses each sample by fit- ting it to neural function, with quantized and entropy-coded parameters forming the bit cost. As shown in Fig. 2 (a), standard overfitted codec models a data point S using a function gw and latent vector This fitting process is indicated by F, while Q and represent quantization and entropy coding. At decoding, S is reconstructed using the quantized Iw and 2 S = 9w 9w-(2), (2), where hat notation denotes quantized variables. This results in an average distortion D Es Ep. [d(S, 9w (2)) at rate
(W1
QiA
QiA
{x²)
{r"}
F
Modular region-based codec Figure 2: From standard overfitted codec to MoRIC.
(a). Standard overfitted codec
R E.s-p loga ps log2 p W) + R,b]
where d denotes distortion metric and (2))) is
the estimated distribution of & using an estimation model dh. In practice, entropy coding of relies on a lightweight auto-regressive entropy model (ARM) 30 for distribution estimation, introducing additional cost Rg for transmitting its parameters.
Modular layered codec. Taking overfitting to more fine-grained level, we propose a modular region-based codec (MoRIC) that assigns dedicated INRs to distinct regions a data sample (see Fig. 2 (b)). Specifically, MoRIC first partitions the input image S into N mutually exclusive re- gions (Sa ..... S.N J. where the position of region S within the image is denoted by æ². Each S is fitted using a distinet neural function Iw and a latent vector z both of which are quan- tized and entropy-coded, The region contours T² are compressed using chain coding scheme C()). During decoding, r' guide the selection of parameter sets (W 2²} via selection function S-)), enabling the reconstruction region-by-region as = U Iw (2t, xx), where V denotes the region merging operation. The expected distortion is D = Es-p,
d(S,)) and the rate is
R = Egup,
== loga P. (2t) log, p( (W+) log, p(T)) + R
While each region uses
different W shared ARM is employed to improve compression efficiency.
3.2 Adaptive contour compression with C* coding
Inspired by [1], we propose an adaptive chain coding method (called C* coding) for efficient contour compression in region- based overfitted codecs. It ensures (a) semantic coverage of tar- get objects against artifacts, (b) robustness to high-curvature via adaptive dilation, and (c) balanced RD trade-off. As illustrated in Fig. C* coding comprises four key modules: gle matching, global resetting, offset adaptation, and contour dilation.
Angle matching
Global resetting
Offset adaption 6 Pe11
Contour dilation
Canser
E. My
Figure 3: Illustration of C coding.
Lossy contour compression. Starting from an initial point with step length 7 (in pixels) and initial angle do. the direction space is evenly

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Bitstroam
ARM
Nergo
combet
Entropy
Figure 4: Workflow of MoRIC: the image partitioned into N regions, each compressed using distinct LSN Dyrr modulated with a shared GMN fg.
divided into Mo angles for the next step. At each step, compute the offset angle 9, between the nearest angle candidate and the contour point located -ddittance ahead, along with its distance offset d. Based d, global reset is applied to update Mc+1 and Φ1+1 if the previous offset adjustment is considered too large. Subsequently, Φx+1 is adaptively adjusted according to 9g for better angle-matching in the step. After each coding round, dilation is selectively applied if the target region is not well-covered by the contour, based on an error threshold c, followed by re-coding. This iterative process produces the final lossy contour f. The bit cost per step is (Mg) accounting for angle selection and reset signaling. A move-to-front (MTF) transform [18,6] [ is further applied to reduce redundancy. See Algorithm I and Fig. 12 Appendix D.2 for details.
and M 8, followed by an MTF transform. To further reduce bit cost, we additionally incorporate three alternative strategies: (I) shared vertex descriptions via vertex chain coding (VCC) [8, (2) directional encoding based on prior directions using three orthogonal chain codes (3OT) [42), and (3) angular difference encoding through normalized angle difference chain coding (NAD) [59]. All schemes will be open-sourced, Appendix D.2 and supplementary materials for more details.
Lossless contour compression. For lossless coding, we fix
3.3 MoRIC architecture
As shown in Fig. 4 the MoRIC architecture comprises four key components: local synthesis net- works (LSNs), a global modulation network (GMN), latent modulations (2*), and shared ARM (rw)). Specifically, each LSN (fw=) is optimized for designated region to map local coordinates to RGB values. The GMN (Se) is globally optimized across regions to modulate each LSS layer by layer. Latent modulations 2² are learnable vectors, and ARM is shared entropy model used to compress all z² More architectural and algorithmic details are provided Appendix D
Local synthesis networks (LSNs). For each region, the corresponding LSN takes the coordinates within the contour (x') input and reconstructs their pixel intensities. shown in Fig, each gw consists of L, = 4 convolutional layers, each followed by a shared modulator M(-)). At each layer, MM-) concatenates the output of the previous layer with modulation vector provided by fe. and passes it through shared-weight MI.P to generate the next-layer input.
key innovation here is that the parameters of MM.) are shared between regions, which offers: (a) reduced bitrate via parameter sharing, (b) coarse-to-fine multiscale modulation across layers, and (c) implicit fusion of local and global features. This design simplifies local coding while injecting global context, boosting compression efficiency and RD performance.
Latent modulation. For the i-th region, latent modulation is defined z² 2
{2)
where each 2 E カ- is learnable vector with the same spatial shape as the region i, corresponding to 2 - downsampling of its coordinates, with K* being the pixel count of region i.

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Contour
Shared modulator
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Globally
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Latent modulaaiions
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Concetmnat
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Figure 5: Illustration of the proposed PCM mechanism. Red blocks with shared icons indicate parameter-shared components across regions. Each LSN modulated using multi-scale features generated by fg from the corresponding latent vector 2
Global modulation network (GMN). As illustrated in Fig. 5 GMN fo consists of an upsampling module followed by I.m 4 convolutional layers. It takes the quantized g' as input and generates hierarchical modulation vectors for each LSN. Specifically, 2 is first upsampled via transposed convolutions to form U us; " E z with each uz - Upsumple($)) ($)) E zk' The
resulting U is then processed through successive convolutional layers as: U = S (Uk where f/ and U denote the operation and output at the k-th layer of So for the i-th region, respectively.
Progressive Concatenated Modulation (PCM). To inject global context into local synthesis in coarse-to-fine manner, propose the PCM mechanism. PCM progressively concatenates latent- derived features to enable multiscale modulation across regions. For the k-th layer of gwe, the modulation vector is defined as Mt Concatenate( ...... U At each LSN layer, modulation operation MM-) concatenates M with the current layer output and processes it through shared- weight MLP to produce the input for the next layer. Intuitively, this design consistently injects global context and allows each region to dynamically refine its representation. Notably, MoRIC with PCM serves as general framework that can support alternative modulation strategies, such as 40 36
3.4 RD optimization
To balance the RD trade-off, MoRIC with an N-region configuration is trained to fit each data point into the parameter set: A sb. B, U (z*, T², wi) }. by minimizing the following loss:
((2) = E [d(s$ St) x where St Iws (fo()*), x*) denotes the reconstruction of the i-th region, R(2*) is the rate term of 2t, and À is hyperparameter that controls the RD trade-off.
During training, latent modulation z undergoes soft-rounding with Kumaraswamy noise, while hard-rounding used inference. The loss excludes rate terms for T³ and (0, W }) due to their minor contributions. In practice, T' encoded using C* coding, and network parameters are quantized and entropy-coder via non-learned distribution. All components are included in the final bitstream. Implementation details are provided in Appendix [D4]
3.5 Advantages of MoRIC
Single-object compression, MoRIC can be especially promising for exed-background (static camera) scenarios like surveillance systems, where detected objects of arbitrary shapes are compressed individually, while the fixed background can be assumed be known by the receiver.

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42
20-
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3D va 2/T 32.1
BD-atte VTH 35.1
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MatUE: touns
MUCC+
12
MoRIC (ours)
MUC+
Nasi
16
24
66
(pppi(11
12
Decading compliddy SMACk corget (44)
(a) Davis datasct
(b) Kodak dataset
(c) Davis dataset
Figure 6: RD performance for single-object compression. (a-b) curve and BD rate on Davis and
Kodak datasets, respectively. (c) BDDrate vs. decoding complexity on Davis dataset.
Table 1: Effect of C* coding for contour compres- sion across various granularity levels.
2/h
Step length
IoU (%)
bpp
RD performance
Total bpp
PSNR (dB)
100%
0.0637
0.213
24.76
67%
4
93.66%
0.0409
0.621
32.01
1.03
0.192
24.46
91.07%
0.0244
Latest
Network
Cristooz
Compression overhead breakdown of MoRIC for single-object compression.
Figure 7:
10
87.31 9%
0.0140
0.621
31.80
Region-wise compression. MoRIC establishes a new paradigm for overfitted codecs through modular, region-wise design that improves the RD performance, enables flexible complexity control across regions, and offers potential for accelerated encoding (similarly to 43 35 34
Scalable layered compression. MoRIC reveals that overfitted codecs can achieve semantic gen- eralizability: its shared PCM and ARM enable layered, coarse-to-fine compression, allowing local INRs to progressively infer and refine other regions via region-wise transmission.
Experimental results
evaluate MoRIC on DAVIS 39] Kodak (28] and CLIC2020 datasets (2 comparing it with
classical codecs (VTM 9 autoencoder-based neural codecs (EVC [54] MLIC (26)). and recent
overfitted codecs (7), COOL-CHIC [32) and LotteryCode:(56) RD performance is assessed using peak signal-to- torllltt--ooooe to-noie ratio (PSNR) on RGB channels and BD-rate 20 while MACs per pixel and coding latency are reported to evaluate decoding complexity and coding efficiency. Region masks directly taken from DAVIS and generated for Kodak using SAM2 4 Additional experiments, datasets, and visualizations are provided the Appendix and supplementary materials. We begin with the single-object compression task, which focuses precise compression of targeted regions objects (experimental setup detailed in Appendix E.2) Next, we evaluate MoRIC on the standard full image compression task. Finally, explore layered compression scenario, where the source is progressively encoded and reconstructed in coarse-to-fine manner.
4.1 Single-object compression
RD performance. As shown in Figs. ba and 6b MoRIC achieves state-of-the-ar (SOTA) RD performance on DAVIS and Kodak for single-object compression, outperforming MLIC+ (current leading neural codec) with BD-rate improvements of -100 -00.43% and 110.73% over VTM-19.1. By overfitting only target pixels, it ensures accurate reconstruction with reduced computation. Although less competitive at very low bitrates due to contour and network overhead, it still outperforms other

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cot V 2901
PSWN (480
40
MUC+-
15
MUCC+
MUC++
VTM-15.1
MoRIC Jourst
MoRIC (ours)
VIM-19
(edeph)
(bpo)
(a) Davis dataset
(b) Kodak dataset
(c) CLIC2020 dataset
Figure 8: RD performance with BD-rate results for standard image compression on (a) Davis, (b)
Kodak, and (c) CLIC2020 datasets.
SD moe- OrTW (S0
BD rooo Vs VTM 19 (SS 1
CCV4
Notice
DyCG
(adapt)
CVC
"FACC""
lours)
SPCC
NaC+
150
-60
12
Decodin complextt torpet (4e)
Decoding complexty (MKS carger skell
caly targut piecl
(a) Davis dataset
(b) Kodak dataset
(c) CLIC2020 dataset
Figure 9: Trade-off between RD performance and decoding complexity (a) Davis. (b) Kodak, and
(c) CLIC2020 datasets.
overfitted codecs thanks to its shared-layer design. Additional results and ablations in Figs 15 and 16 the Appendix further validate the effectiveness of our design.
Decoding efficiency. MoRIC offers low decoding complexity in single-object compression, achiev- ing better RD performance with fewer than 800 MACs/pixel, far lower than all AE-based codecs (see
Fig. 6c detailed analysis of decoding complexity, latency, and BD-rate provided in Fig and Table in the Appendix. These results underscore the efficiency of region-basee compression by overfitting only target pixels for accurate and efficient reconstruction.
Effeet of contour compression. To evaluate the impact of C* coding, T intersection- over-union (IoU), contour bit cost, and RD performance. As step length increases, the bit cost drops, with RD performance remaining acceptable at low bpp values, but degrading sharply at high bpp. highlighting the benefit of lossy contour coding in low-bpp regimes and the importance of contour accuracy at high bpp. Fig. [ further breaks down compression overhead across various bitrates. showing that contour bits dominate at low bpp, but are negligible at high bitrates, validating the efficiency of our approach. More details and visualization C* coding are provided in the Appendix.
4.2 Full image compression
RD performance. As shown in Figs. Sa formance among overfitted codecs for the standard full image compression task (as opposed to compressing only the region/object of interest considered above). achieves -5.0% BD-rate reduction over C3 on Kodak. 5.51%% over COOL-CHIP (v4) on DAVIS, and -5.48% over C3 on CLIC2020. Notably, MoRIC surpasses 1TM-19.1 on the Kodak and CLIC2020 datasets with BD-rate reductions of -2.99% and - 10.58%, respectively, establishing a new benchmark among overfitted codecs. comparison,
8c MoRIC achieves state-of-the-ar RD per-
previous state-of-the-an LotteryCodec achieved -0.66% and -9.79%. Like other overfitted codecs, MoRIC still falls short of leading neural codecs MLIC+ in terms of the RD performance, but achieves over 100x lower decoding complexity. Additional results and ablations in the Appendix (Figs 2022 and Tables.
12 further validate the effectiveness of

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Ground truth
Region mask
LSN1 output
LSN2 output
Layer O (gge
Layer 1 (0we)
Layer (grz))
0.088/16.1300453
0.094/20.04/0.499
0.101/30.72/03366
Figure 11: Layered compression with MoRIC: The background LSN gwo is transmitted first (layer 0), followed by Iw (blue region, layer 1) and Jw> (red region, layer 2). The first row shows outputs from each individual LSN; the second row shows the cumulative reconstructions after each layer. Bitrate in bits-per-pixel (bpp)/ PSNR (dBy/ LPIPS scores are reported below each image.
our design. Interestingly, lossy contour compression reduces the bitrate with minimal impact distortion, thanks to global-local modulation design across regions.
Effect of number of regions. We conduct experiments under different region configurations (over 10 Kodak im- ages). As shown in Fig. I0] increasing the number of regions improves the RD performance, with the largest gain from to 2 regions. Since the gains are diminish- ing with N while the complexity increases, we consider up to 3 regions for strong performance with manageable overhead. Detailed results are provided in Fig. 24 with visualization in Fig. i5 in the Appendix.
MORIC (66 166141
rare vs, 1981199 (8/141
MosICC bsingte) buseline
3.-
VTH baseline
Decoding efficiency. MoRIC achieves strong RD perfor- mance with low decoding complexity (Fig. D.. Compared to other overfitted codees, it achieves superior RD per- formance with fewer decoding operations. To the best of our knowledge, MoRIC is the first neural codec surpass VTM on Kodak in RD performance (-2%79% BD-rate) while maintaining low decoding complexity (below 2000 MACs/pixel). Additional results decoding complexity, coding latency, ablation study, and BD-rate across different datasets are provided in Fig 9 and Table
Region number McRIC
DD vp. VT9:3.
3D-rate va. Venii Singlal
Figure 10: Effect of region numbers.
10
4.3 Scalable layered compression
As shown in Figs D and 11 MoRIC naturally supports layered, coarse-to-fine compression by first transmitting the background LSS to produce a coarse reconstruction, followed by region-specific LSNSs for progressive refinement. Notably, even with only the background LSN, object structure and semantics remain clearly recognizable despite color inaccuracies, highlighting the ability of MoRIC to generalize between regions. As more bits allocated for additional LSNs with region-specific refinement, color and texture details improve progressively.
More examples in Figs. 28 and 29 reveal that common features like shared colors are captured by the global modulator, enabling local LSNs to infer them correctly. In contrast, region-speciff features and colors require dedicated INRs for precise refinement. From Fig, 30) we observe that cross-region inference more challenging in the low-bpp regime, while richer latent modulations higher bpp enable more accurate context and feature reconstruction. This layered compression capability of MoRIC especially beneficial for high-resolution images with many I.SNs, enabling progressive refinement and efficient and controllable region-wise reconstruction.

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Conclusion
We presented MoRIC, a modular region- based implicit codee that compresses images via region-wise overfitting. By assigning dedicated networks to distinct regions, MoRIC enables fine-grae see-ggaandd RD control and precise single-object compression. Our approach integrates adaptive chain coding for efficient contour compression and employs GMN for coarse-to-fine multiscale modulation of local synthesis. MoRIC achieves the SOTA performance both single-object and full image compression tasks with low decoding complexity. Furthermore, it naturally introduces layered compression capabilities resulting in more scalable and flexible overfitted codecs for real-world applications.
Limitations. While the region-based design of MoRIC helps with convergence, its high encoding complexity remains a challenge. Therefore, like other overfitted codecs, MoRIC is especially beneficial for multi-user streaming applications, supporting one-time encoding and repeated decoding. Potential acceleration strategies include meta-learning and region- wise mixeddppeeisiin training.
Future work. MoRIC be extended to video coding by leveraging contour correlations and sharing modulations across adjacent groups of frames (GoFs), improving the RD performance and convergence speed. While it currently SAM2 for region selection, future work can integrate segmentation into the coding process to explore trade-offs between granularity and performance.
Acknowledgments and Disclosure of Funding
We acknowledge funding from the UKRI for the projects AI-R (ERC Consolidator Grant, EP/X030806/1) and INFORMED-AL (EP/Y028732/1).
Author contribution
D.G. conceived and supervised the project, and developed its overall vision. H.W. implemented the initial codebase and designed the experiments. G.L. designed the chain-coding, local-global mechanism, and optimized performance. H.W. and D.G. wrote and revised the paper. These authors contributed equally and are listed alphabetically: G. Li and H. Wu.
References
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Guidelines:
The answer NA means that the method development in this research does not involve LLMs as any important, original, or non-standard components.
Please refer to our LLM policy for what should or should not be described.
21

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Appendix Contents
Open resources
Broader impacts
Baseline implementation
D MoRIC implementation
Additional experiments and visualizations
A Open resources
(a) Datasets. We open-source our region-based coding dataset, including the DAVIS (18 images) used in our experiments and our region segmentation results for the Kodak (24 images) and CLIC (41 images) datasets. Additionally, we provide a new beee-bbacggound dataset to support future research on region-based compression, particularly in backgroddd scenarios.
(b) Adaptive chain coding method. We open-source both lossy and lossless variants of C" to facilitate future research and development for modular region-based codec (which is included the supplementary materials and to be released publicly after review). Notably, C* coding may be of independent interest for broader INR-based research beyond compression.
(c) Code and checkpoints.
Code and checkpoints are released in the project page.
B Broader impacts
This work presents a technical contribution in image compression with no immediate societal impact. Nonetheless, potential downstream effects may arise depending application context.
Positive impacts (1). Efficiency: Its ultra-low decoding complexity supports energy- -effeceef,,ientt,, scalable deployment in bandwidtth-constrinned settings like loT and mobile devices, especially in multi-user streaming scenarios, significantly reducing the energy footprint of edge devices in the future. (2). Privacy: Region-based compression enables selective transmission and reconstruction, supporting privacy-preserving
(e.g., face masking). (3). Semantic-aware content delivery: Layered, region-based decoding benefits adaptive streaming and semantic-level rendering in AR/VR.
Potential negative impacts However, region-based compression could also be misused to selec- tively manipulate or obscure image content. We encourage future work integrate safeguards such as integrity verification and explainable compression decisions. All datasets used are publicly available, and we release our models and code to promote transparency and reproducibility.
C Baseline implementation
We evaluate method on Davis and Kodak, where Davis standard benchmark featuring salient object regions, and Kodak standard dataset for image compression task. A detailed descriptions of the data used (including their masks) are provided in supplementary materials. MoRIC is compared against classical codec. VTM [9]. as well as autoencoder--assee neural codecs: EVC (54) (optimized RD performance with low decoding complexity). and MLIC++ 25 (statc-of-the-art neural codec). Additionally, we compare with overfitted INR-based codecs such as C3 27 (state-of-the-ae
overfitted image codec) and COOL-CHICV4 (32 (an optimized version of COOL-CHI version with competitive performance from C3), and the most advanced LotteryCodee [56]. We measure PSNR
on RGB channels and quantify RD performance using the BD-rate metric 20 The baseline results were obtained using their official implementations papers. For VTM, we use the CompressAl library 4 to implement VTM-19.1 (YUV 10 bits), with additional details (code and datapoints) provided in the supplementary materials.
directly using the reported results from their
22

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D MoRIC implementation
D.I Region selection
For single-object compression, we directly use the provided region masks from the DAVIS dataset, while for the Kodak dataset, regions are manually selected using SAM2. The selection focuses on areas of contrast saliency. We emphasize that the region selection in this work serves to investigate the potential region-based compression. The masks are not optimized and can be further refined, with significant performance improvements expected. All masked datasets used in our experiments are provided in the supplementary material with open access to support future research on region-based compression.
D.2 Adaptive region contour compression using C* coding
C coding is tailored for region-based overfitted codecs. where we consider three main objectives:
(a) Semantic coverage: ensuring the full inclusion of the target object region to preserve semantic integrity and minimize object reconstruction artifacts. typical region-based coding, the image split into foreground and background. By covering the entire object, C* avoids boundary artifacts over objects, especially beneficial for the exed-background scenarios. Background areas, which are generally less critical, can be approximated by the INR with minimal object-quality loss.
(b) Robustness to curvature: applying adaptive dilation the coding process can simply prevent encoding failures, caused by high-curvature contours that may lead to ambiguous or looping paths. This simple yet effective mechanism enhances reliability region- based coding.
(c) RD trade-off: balancing contour accuracy and compression cost is crucial in overfitted codec design. While lossy contours (without covering target region) may save bitrate by omitting parts of the object, they often lead to significant degradation in distortion performance.
Next, we detail the proposed C* coding scheme, as illustrated in Fig 12 and Algorithn
Lossy compression. At each step, we compute the offset angle 6g between the current point and the contour point T step-length ahead, i.e., the intersection with a radius-T circle-and select the closest discrete angle & as the next direction. Meanwhile, offset distance d is also computed. M,
Based on d, we determine whether the offset is too large, indicating the coding step has drifted from the contour. so, we perform a global reset by setting the angle to 2 and increasing directional resolution. This is triggered when 27 sin 41) After adjustment step, ø and M reset to their initial values.
After global reset, the angle is adapted based on the accumulated average offist 0, If 0, < 2 the angle is halved, indicating the current direction is sufficiently accurate. If - the angle is doubled to allow finer directional correction, and 0t is reset zero. Otherwise, the angle remains unchanged: @x+1 = Φt-
After each coding round, dilation step is selectively applied to ensure the contour fully encloses the target region. This prevents semantic loss and significant RD degradation caused by missing pixels outside the contour. Specifically, algorithm is presented in Algorithm
3 kernel is used dilate the contour. A more detailed
Lossless compression. For the lossless compression approach, we refer to our supplementary materials, with detailed instructions and codes.
D.3 Region-based latent configurations
Each z² consists of L learnable multi-resolution vectors, defined as 2' 2 {22 z......... = where zj E R corresponds the j-th resolution level for the i-th region, and K* denotes the number of pixels within that region. Specifically, 2 matches the spatial resolution of the i-th region, and each subsequent z} is constructed by successively downsampling by factor of 2 x 2, so that 2 is
23

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3 sT 4
2m, 16
91-1 90
M411 = Mg
Global resetting
Angle matching
Eg
Offset adaption
Oel
Oftsot?
(c+1)
Sd 0441
der dc+1
Current
40
g.
esch chann
Contour dilation
codirg rourd
Coding
LO MERTI
Figure 12: Illustration of the proposed C coding, with details in each block.
reduced by 44-1, In practice, all 2) are initialized with the full image resolution Hx where H and W are the original image height and width. A binary region mask is applied to isolate the area defined by the contour, which is then downsampled to construct each zj. During training of each region, gradients are stopped for latent outside the region to ensure that only relevant networks and latent updated. This allows efficient selection of latent features based coordinates.
D.4 Quantization and entropy coding details
In MoRIC, latent modulations z², and parameters LSN for each region W parameters of ARM and GMN go through quantization and entropy coding for compression, using standard methods, as More details can seen the Table, 2
22
Quantization-aware optimization, Inspired by we also adopt two-stage quantization-awan optimization approach for each z². During training, is optimized a continuous space with quantization approximated via Kumaraswamy noise, enabling differentiability. At inference, uniform quantization with hard-rounding is applied as:
(Tr(2t) + Ukam: Training Stage 10(=),
Training Stage I & Inference Stage,
ST is soft-rounding with temperature T. Q is hard-rounding, and ukum Kumaraswamy noise. The temperature and noise are annealed to shift from peaked to uniform distributions throughout training.
we adopt factorized auto-regressive model rwp estimate the distribution of each ş for entropy coding. For each i-th region, every latent element of #t (the j-th element of z{) is conditioned on C' spatially neighboring elements chjj E 7 as:
Entropy coding. Similar prior works 30 38),
(=))
II
po (2k (ck.s)
(2)
24

---

Algorithm C* coding of MoRIC
Input:
Initial angle do. angle divisions Mo. and step length T, error threshold initial f total iteration number K, accumulated step number & 0. dilation kernel rs-).
Output: Bitstream contour by.
I: for each iteration among the K do for each t-th step until the coding
completed do if > 22'222issm sin( [TM,-1) then
3:
01, . + {1,, current position).
# Compute the offset angle and distance
5:
6i 2m, Mr 16
# Need more accurate divisions Reset angle and divisions # Global resetting end
6:
@c+1 0u, M411 Mu
7:
end if
8:
# Update current average offiset
9:
i < M[M,-1]
then
10:
Φc41 206
Offset small, decrease the angle
11:
else if 0, > [Mc-1] then
12:
Φc+1 = 20c, 02 = k 0,
Offset large, increase angle
13:
else
14:
6141 ót.
15:
end if
# Off'set adaption end
16:
end for
17:
< {T.
Compute the error of object contour
18:
if > co then
19:
$ + x(f).
# Dilation the contour
20: else
21:
Return and break the loop
Finish contour coding
22: end if
23:
end for
24: b, MTFT(()
# Move-to-front transformation
where (2t) is modeled by an integrated Laplace distribution. The expectation and scale parameters are estimated via context elements y L(ukk ok.)). where pig. ok,, Tap (ck..) With this estimated distribution of 2², a range coding algorithm is used (range-coder in PyPI) to compress 2t The resulting rate contributed by 2² is then given by:
R(2*) = log2 Pe (2*) = log2 II P (eo
Σ kjj
logg Pe (
(3)
kjj
Then the total bit cost from the latent modulations can expressed b₂ - 12(2)).
Parameter compression. The parameters of neural networks: each LSN, GMN, and ARM are compressed with quantization operations and an unlearnable entropy model. Specifically, we first quantize W', 0, and &e using a scalar quantizer Q(- A) with step size A, defined as:
W Q(W Aw.), θ Q(0, Ae), and +B Q(v, Av).
The quantized parameters W i and a are then entropy-coded, where the discrete distribution of each quantized parameter is modeled by a continuous Laplace distribution. For example, the probability of a quantized parameter from 0 (similarly for ab and Wi) is given by:
A.+05
p((.)
(0)dd,
with g stddev ④)))
(5)
0..
Then the total rate contribution from neural parameters can be expressed as:
PMLP Σ
Rw + Ri + Rgg Σ
loga ((W2) - Σ loga p(0x)-
Σ Loggp(15 (6)
1=0
k,i
25

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Table 2: Hyper-parameter settings
Hyper parameter Values of A
Initial values
Final values
2
Se
de
2e
5e
2e
Quantization Stage
Number of encoding steps Learning rate 3
10a
10-2
0
Scheduler for learning rate
Cosine scheduler
Temperature for soft rounding
0.3
0.1
Noise strength for Kumaraswamy noise Scheduler for Soft-rounding and Kumaraswamy noise
2.0
1.0
I Linear scheduler
Quantization Stage II
Number encoding steps
10a
Learinng
10-4
10-8
Decay learning rate if loss not improved for this many steps
40
Decay factor
0.8
Temperature for soft rounding
10-4
Architecture Entropy model
Alternative values of for ARM-c model
e E (8/16/24/32)
Activation function
GELU
Log-scale of Laplace is shifted before exp
4 10- 150
Scale parameter Laplace is clipped
Architecture Latent modulations
Values
Number of latent vectors
Initialization of
Architecture Global Modulation Network
Single-object vs. Standard 4 x 4 vs. 8
Upsampling kernel
Output channels of the x convolutions
{7 3/5 + 3) vs. {7 18/24/30 3)
Output channels of the 3 x 3 convolutions Modulation vector dimension
{3 +
{3 + 3)
Architecture LSN
Values
Output dimensions of each layer
{2 3 13 [6/8 -+
Output cach shared modulator (ohject) Out-channels each shared modulator (standard)
(24/30 /36 + 33: (27 - 33; (30/36/42 33
greedy search process over quantization steps is conducted to search optimal Awr, Do and Av by minimizing the following RD cost:
N Σ
min AW.ABA
((S"..9::(fo(")) AR(2t)] ARMLP.
Model architecture. We provide the detailed architecture setting for MoRIC in Table.
For the ARM model with e contextual elements as input, denoted as ARM-c model, there are three linear or 1 x convolutional layer, followed by GELU activation functions, with input and output dimension given as (c x c) - GELU + (c x c) - GELU + (c x 2). For the proposed MoRIC, employ {8, 16, 24, 32).
For the GMN model, which uses = layered-resolution latent modulation as the input with I. 4 layers, the input and output dimension are given as: (7 d) GELU + (d x 3) GELU + (3 x 3) + GELU + (3 x 3). For the proposed MoRIC, we employ d E {3.5) 5) for single-object compression and d = {18/ /2/0///0 for standard image compression such Kodak and CLIC2020 dataset.
For the LSN model, which maps pixel coordinates to their RGB values with L, 4 layers, the input
and output dimension are given as: (2 3) > GELU ([3+ + mi x 3) - GELU - (3 3) + GELU + - ([3 m2] x 3) + GELU + (3 x 3) + GELU + - (3 + mg] x 3) + GELU + (3 x 3) Note that here the orange part shared modulators (one MLP layer). For a PCM design, = + d (concatenation of first two layer output of GMN), m2 = 3 + d + 3 (concatenation of first three layer output of GMN), ma = + d + 3 (concatenation GMN), For single-object compression, the modulator is shared across layers (then we remove the
first four layer output of
26

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Algorithm 2 Encoding stage of the MoRIC
Source image S, coordinate vector for each region x², Learning rates for Stage and II: a, 8, Region latent for modulations (z"), and networks (Region LSN W*, GMN 0*, and ARM zb),
Input:
Cosine scheduler for learning rate for Stage I and II: Ti, T2,
Linear scheduler for soft-rounding temperature T and Kumaraswamy noise Ukum strength for Stage I and II: l1,
l2, and Greedy search for quantization step: G. Output: Bits stream of bz, br, bw, bø, by.
(S* ...., S {T² ...., , (ar (.""....,.")
Partition the source into N regions
=' (2i.
with each z/ E O
Initialize latent for each region Configure each LSN and GMN from Kaiming initialization
3: W' yuk 0 Us
4: for the k-step within the Stage do
i-th region within the N regions
6:
2. =T());) + Ukumm
# Quantization-awar training
S: = Sw- (fo(")))))
# Modulate the local reconstruction
8:
end for
(( Σm= ci(s", St) + An(ES)]
Compute the cost loss function
10:
- 0 - aVaL.
# Update the GMN # Update the latent for each local region # Update LSN for each region # Update ARM
11:
x¹ + + -
12:
W'+ a wil.
13:
$ - --v-aV+4
14:
k). 15: T= (T, Ukum (1kkum
# Schedule learning rate # Schedule noise strength
16: end for
17:
the k-th step within the Stage do for each i-th region within the N regions do
18:
19:
2¹ = Q(=").
# Hard rounding
20:
S. 9w (2t),
# Modulate the local reconstruction
21:
end for
22:
((22) EmO
ddss" ) + AH(2))]
Compute the RD cost loss function
23:
0 - 0 VoL,
# Update the GMN # Update the latent for cach local region # Update the LSN for each region # Update ARM # Schedule Icarning rate Schedule noise strength
24:
x² *+* -
25:
W + --W'- yV -Wiiihh
26:
b + ---
27:
3 (3,,)), B (B, k).
28:
T (TT, k). Wkum la (ukkum: k)).
29: end for
30: b. Σn A(Q(z*)),
Quantization and entropy coding over = Adaptive chain coding for contours Search for optimal quantization step networks Quantization and entropy coding over
31: b, = Σ. C(T+),
32: Ao. Awi, Ar G(O, W ()
33: 0o AlQ(O, Ag))
34: bw IN A(Q(Wi, (A:))
Quantization and entropy coding over W # Quantization and entropy coding over zp
35: b A(Q( A
Algorithm 3 Decoding stage of the MoRIC
Input: Bits stream of bz, br. bw, be, by-
Output: Reconstruction of image $.
** _² + C(b)),
Chain-decoded contour with its coordinates Entropy-decoded and dequantized latent modulation deocded network parameters
2: 2t Q(A(b=)).
3: d Q(A(bb)), ē = Q(A(bo)), W Q(A(b
4: for each i-th region within the regions do
5: S (f=
Reconstruct the local region
6: end for
S= UN S St.
Merge source image
concatenation for m. = m² my = dl for less parameters); for standard image compression, the modulatoris is shared across regions.
27

---

Pseudocode for the algorithm. This section provides the encoding and decoding procedures of MoRIC, presented Algorithm 2 and Algorithm respectively. We use orange to indicate GMN- related optimization, purple for ARM-related optimization, blue for local region-specific optimization, red for chain coding, and green for LSSN optimization.
Ground truth
with
Reconstruction
with T 10
Reconstruction
bpp/IoU bpp/PSNR
0.139 / 92.11%
0.139/23.11
0.131/88.95%
0.131/23.24
bpp/IoU or bpp/PSNR
0.167 / 94.89%
0.167/25.09
0.135/87.32%
0.135/25:12
bpp/IoU or bpp/PSNR
0.310 93.59%
0.310/23.99
0.281/84.30%
0.281/23.70
Ground truth
with
Reconstruction
with
Reconstruction
bpp/IoU or bpp/PSNR
0.197 / 94.75%
0.197/25.46
0.189/90.61%
0.189/25.00
bpp/IoU or bpp/PSNR
0.208 / 93.15%
0.208/25.15
0.193/83.23%
0.193/25.10
(b)
Visualization of the proposed C' coding under varying step lengths T (larger T resulting Figure 13:
in coarser contours) in the low-bpp regime (A 4e -2), with corresponding bpp. IoU, and PSNR.
E
Additional experiments and visualizations
E.1
Contour compression using C* coding
This section presents visualizations the proposed C* coding under varying step lengths across different bitrate. C* coding approximates object contours using polygonal chains. Starting from an initial point, each contour segment is encoded by a fixed step length and quantized offset angle relative to the previous direction.
28

---

As shown in Fig. 13 from the view of RD performance, in the low-bpp regime, coarse C" coding achieves comparable PSNR with significantly lower bit cost. Similarly, high-bpp regime result visualized in Fig. 14 We can see that for high-bpp regime, more-accurate contour compression approach affordable, resulting
better RD performance. We want to note that, the adaptive step length 7 allows flexibility to meet user-specific needs. For instance, users prioritizing semantic accuracy or precise contours can opt for a smaller I the expense of additional bits. Additional experiments about the chain-coding are also provided in Table 3
Ground truth
with
Reconstruction
with 7 Reconstruction
bpp/IoU bpp/PSNR
0.710 / 92.11%
0.710/30.78
0.703/88.95%
0.703/30.59
bpp/IoU or bpp/PSNR
0.496 / 94.89%
0.496/31.66
0.490/87.32%
0.490/31668
upp/IoU or bpp/PSNR
0.760 / 93.59%
0.760/32.21
0.728/84.30%
0.728/3168
Ground truth
with
Reconstruction
i with
Reconstruction
bpp/IoU or bpp/PSNR
0.573 / 94.75%
0.573/32.62
0.595/90.61%
0.595/32.50
bpp/IoU or bpp/PSNR
0.570 / 93.15%
0.570/32.78
0.193/83.23%
0.589/32.54
(b)
Figure 14: Visualization of the proposed C* coding under varying step lengths the high-bpp
regime (A 2e 23,3), with corresponding bpp, IoU, and PSNR.
Table 3: Contour coding efficiency on Kodak dataset (kodim23), evaluated by error rate/bit cost. Lossless chain coding
0%/1641
Quality values of VTM Performance of VTM
10
36
56 6.62%/1966
0%/9128
1.48%/680 /6864
Step length of C* Performance of C*
5
10
15
0.66%/890
1.17%/366
2.08%/251
29

---

40
-15
38
-10
BD-rate vs VTM 19.1
-5
PSNR (dB) (t)
34
32
MoRIC adapt. (ours)
MoRIC tixed (ours)
10
30
MLIC++
CC-v4-con
15
28
CC-v4-rec
20
26
C3-rec
EVC-L
EVC-M
24
EVC-S
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Rate (bpp) (4)
Figure 15: RD curve and BD-rate with more baselines for single-object compression on Davis.
-15
38
-10
36
BD-rate VS VTM 161
PSNR (dB) (1)
32
MoRIC adapt. (ours)
10
MoRIC fixed (ours)
30
MLIC+
15
VTM-19.1
28
CC-v4-rec
20
C3-rec
EVC-L
25
26
EVC-M
EVC-S
30
0.2
0.4
0.6
0.8
1.0
1.2
Rate (bpp) (4)
Figure 16: RD curve and BD-rate with more baselines for single-object compression Kodak.
E.2 Single-object compression
Experiment setup Single-object compression task only considers the compression over target region. Specifically, for AE-based codecs in the single-object compression task, the target object is cropped out using the smallest enclosing rectangle, with all pixels outside the target region set to zero for baseline methods, effectively allowing AE-based codecs implicitly encode the contour and achieve optimal performance. For overfitted codecs, we evaluate (1) COOL-CHIC-và combined with our precise contour coding (denoted as CC-v4-contour) to assess architectural gains, and (2) C3/CCv4 combined with minimal bounding-box contour (C3-rec; CCv4-rec) as alternative baseline.
Additional experiments For more detailed experiments for single-object compression task, Figs. 15 16 and Table g present detailed RD performance, along with ablations on applying our chain coding to other overfitted codecs and adaptive configurations, which further validates the effectiveness of our design. Additional results of decoding complexity, encoding latency, and BD-rate provided
30

---

Table 4: Detailed BD vs.
VTM-19.1 for single-object compression task.
Dataset
MoRIC
MLIC
EVC-S
EVC-M
EVC-L
CC V4
C3
Davis dataset
-10.43%
-9.65%
27.92%
20.39%
18.14%
16.31%
23.48%
Kodak dataset
-10.73%
-0..3%%
26.28%
16.57%
13.70%
10.69%
25.29%
Fig 17 and Table We can see that MoRIC can achieve faster decoding but slightly slower encoding in terms of latency for single-object compression.
Table 5: Average coding time for single-object compression the DAVIS dataset using an NVIDIA RTX 3090 GPU and Intel Core 19- 19-10980XE CPU @ 3.00GHz. Orange indicates GPU computation, blue indicates CPU computation, and bold numbers highlight the best results. Models
Encoding time
Decoding time
BD rate
VTM-19.1
21.53 s
136.02 ms
EVC (S/M/L)
10.62/
13. 1.3.72/27.77 ms
9.41/
ms
27.9 27.92% 20.39% 18, 14%
MLIC+
89.71 ms
145.20 ms
-9.65%
C3
11.87 sec
1k steps
141.48 ms
+223.7%%
COOL-CHIC
14.28 sec 1K steps
136.83 ms
+16.31%
MoRIC
17.54 sec / 1k steps
102.53 ms
- -10.43%
BD-rate vs VTM 19.1 in [%6 (4)
EVC-S
BD-rate vs VTM 19.1 in [%) (4)
EVC-S
FVC-M
20
EVC-L
20
EVC-M
EVC-L
10
MoRIC (ours)
MUIC+
-10
-10
12a
10"
10
12"
10"
10"
Decoding complexity [MACs target pixel]
Decoding complexity [MACs / target pixel]
(a) Davis dataset
(b) Kodak dataset
Figure 17: BD-rate vs. decoding complexity for single-object compression.
summary, without incurring high costs and implicit contour learning, MoRIC enables scalable and practical single-object compression with significantly improved RD performance and lowering de- coding complexity. This is especially promising for back-rouk scenarios such as surveillance, where objects can be precisely compressed while background is reused across frames to reduce the overall bitrate.
Visualization
We additionally provide visualizations of MoRIC for the single-object compression
task, as shown in Figs. [8] and 19 Compared with MLIC++, in addition to better RD performance, MoRIC retains more image details (see the dog's 's leg in the picture as example).
31

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Ground truth
MoRIC
MLCC
VTM
bpp:
bpp:
bpp:
PSNR: 32.82
PSNR: 31.58
PSNR:
bpp: 0.649
bpp: 0.64
bpp: 0.68
PSNR: 35.56
PSNR: 33.61
PSNR: 33.61
Figure 18: Visualization of single-object compression on Davis.
Ground truth
MoRIc
MLIC++
VTM
bpp: 0.676
bpp: 0.69
bpp: 0.68 PSNR: 28.79
PSNR: 30.82
PSNR: 29.96
Figure 19: Visualization of single-object compression on Davis.
E.3 Standard full image compression
For more experiments on the standard full image compression task, more detailed RD-curves are given in Figs. 20 21
and Table 6 7 with raw datapoints presented in Table 8 Detailed experimental
results over the effect of region number is given Fig. 24 with visualization provided in Fig. and Table 9 The effect of latent vectors visualized in Figs
26
Complexity and latency comparisons are provided Table. 10 and Fig. 9 Note that the results are based on unoptimized research code and the available hardware; performance is expected to improve with engineering optimizations such as C-API and wavefront decoding. The BD-rate of MoRIC (three-region setting) in Table I0 is evaluated using mix of 1, region settings, as only 10 images
32

---

40
-15
38
-10
BD-rate vs VTM 19.1
PSNR (dB) (1)
-5
MUK++
VTM-19.1
32
MoRIC dapt, (ours)
MoRIC lossy [ours]
lossless
5
30
CC
EVC-L
EVC.M
EVC-S
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Rate (bpp) (1)
Figure 20; RD and BD-rate with more baselines for standard full image compression on Davis.
42
-15
BD-rate VS VTM 19.1
-10
36
-5
PSNR (dB)
MUIC+
34
adapt. (ours)
MoRIC lassy (ours)
0
VIM-19.1
MoRIC lossless (ours)
C3 (adapt.)
EVC-L
28
EVC.M
10
0.2
1.2
Rate (bpp) (4)
Figure 21: RD and BD-rate with baselines for standard full image compression Kodak.
42
-20
BD-rate vs VTM 19.1
38
-10
36
PSNR (dB)
-5
MUC++
MoRIC adapt (ours) lessy (ours)
0
32
VTM-199.1
(adapt.
5
EVC-L
EVC.S
28
0.2
0.6 Rate (bpp) (4)
0.4
0.8
1.0
Figure 22: RD and BD-rate with more baselines for standard full image compression on CLIC2020.
33

---

in the dataset were annotated with three-region masks. Further improvements can be expected with full-dataset annotations.
Overall, our method has a slightly longer encoding time than other overfitted codecs due to its more advanced modulation mechanism, but delivers superior performance. We want note that all reported MoRIC results are based on unoptimized research code. Notably, our decoding modules are now executed serially during latency evaluation; simple parallel execution can substantially reduce runtime. We also expect further improvements through advanced engineering optimizations such as C-API integration and binary arithmetic coding
Table 6: Detailed BD rate vs. VTM-19.1 for standard full image compression task.
Dataset
MoRIC
MoRIC (lossy-fixed)
MoRIC
MLIC
EVC
COOL-CHIC
(lossy-adapt.)
(lossless)
SS/MM/LL
v4
Davis
0.981%
1.94%
2.53%
13.13%
4.43% 7 70.59% 0.58%
6.64%
Dataset
MoRIC
MoRIC (lossy-fieed) -1.24%
MoRIC
MLIC
EVC
C3
(loss--ddapt.) -2.79%
(lossless)
SS/MM/LL
adapt.
Kodak
0.78%
14.96%
7.16% 1.05% -0.73%
2.64%
Table 7: More baselines on Kodak and CLIC datasets.
Kodak dataset
Traditional/INK codec
JEPG2000
HEVC (HM)
BPG
MSCN
VC-INR RECOMBINER
BD-rate VTM-19.1
95.42%
24.90%
22.53 53%
115.91%
73.71%
63.86%
Autoencoder codec
BMS
MBT
CST
WYH
STF
ELIC
BD-rate VTM-19.1
30.3%%
10.85%
3.99%
0.44%
-3.9%%
-6.85%
CLIC2020 dataset dataset
Image codec
BPG
ELIC
Cheng2020 7.22%
WYH
STF -3.22%
CCv4
BD-rate over VTM-19.1
39.28%
-7.04%
4.77%
-6.58%
Table 8: Raw datapoints of MoRIC for standard full image compression task.
Rate [bpp]
PSNR [dB]
Rate [bpp]
PSNR [dB]
Rate [bpp]
PSNR [dB]
0.169
28,834
0.1507
29.118
0.0852
30.628
0.257
30.503
0.3533
32.622
0.1354
32.168
0.390
32.428
0.5217
34.637
0.3534
35.942
0.577
34.503
0.7339
36.701
0.5141
37.544
0.809
36,629
1,0851
39.353
0.7898
39.715
1.010
38.228
1.4173
41.307
1.0722
41.306
1.196
39.511
1.559
41.793
(a) Kodak dataset
(b) CLIC2020 dataset
(c) Davis dataset
Table 9: Bit rate breakdown for MoRIC across region numbers Kodak dataset.
Contour Parametes (%) Lateen
Bl-rate
Bit cost share
Low hpp
Medium bpp
High bpp
MoRIC (single)
0.118I5
0,41885
1.27254
MoRIC (single region)
0% OK%/25.39%//74.0 74.61%
0%/ 14%%/1.866
2.88% 97.11%
0.11940
0.41879
1,24859
MoRIC (N 2 regions)
1.89% 01109/22.01110 01%%/72.0%%
0.544%//8.4199 15541%99910005 09.00%%
0.15% /3. 11%/9/..119///////. 796.71%
-1.29%
MoRIC (N
regions)
0,12067
0.41567
1,24135
-1.72%
3.20% 3.20% /16.71% 77.08%
1.93%/8.555%
(03.555%999...0 590.22%
0.31%%/3.22%//66.oo
34

---

-55
BD-rate vs VTM 19.1
-8.
BD vs VTM 19.1
-50
26-
PSNR (dB)
MS.SSIM
MLIC+
45
MoRIC (ours)
VTM-19.1
14-
MoRIC (Three regions)
VTM-19.1
MoRIC (Two regions)
12
ELIC
40
MoRIC (Siggln reglon)
0.2
0.6
04
10
Rate (bpp) (4)
Rate (bpp) (4)
Figure 23: RD curve with MS SSIM distortion and BI>rrtee for standard full image compres- sion on the Kodak.
Figure 24: RD curve and BD-rate with various number of regions for standard full image pression on the Kodak, where the test set is 10 images and fixed architecture is employed.
Ground
MoRIC (Threa regians)
MoRIC (Two regions)
MoRIC (Single region)
bpg: 0.330
bpp: 0.328
bpp: 0.332
PSNR: 31.44
Figure 25: Effect visualization of the region number for MoRIC: The top row shows reconstruction results, while the bottom row displays the corresponding region masks. As the number of regions increases (adding a dedicated region over the roof and grass as an example), more detailed reconstruc- tions achieved in those specific areas. In contrast, the single-region setting produces relatively coarser reconstructions compared to multi multi-region configurations.
Table 10: Average coding time for standard full image compression on Kodak dataset using an NVIDIA RTX 3090 GPU and Intel Core i9- 19-10XE CPU @ 3.00GHz. Orange indicates GPU computation, blue indicates CPU computation, and bold numbers highlight the best results. Models
Encoding time
Decoding time
BD rate
VTM-19.1
87.13
293.05 ms
EVC (S/M/L)
22.43/36. 22.43/36.19/47.88
19.89 19.89/24.12/331 11/1991191
7.16% 11.5% 0.73%
MLIC++
271.91 ms
364.06 ms
-14.96%
C3 (lixed / adapt)
17.49/21.33 1333 sec 1K steps
283.59 310.54 ms
+4.75% 2.64%
MoRIC (single region)
24.70 1K steps
343.55 ms
0.54%
MoRIC (two region)
26.41
1k steps
408.97
-2.79%
MoRIC (three region)
32.06 see steps
486.48 ms
-2.88%
E.4 Layered compression
Layered coding strategy Towards layered compression scheme, MoRIC first transmits back- ground INRs (LSN-0 for layer-O transmission) to reconstruct coarse structures with some detail
35

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Low bpp 0.123
Figure 26: Reconstruction and visualization of latents for kodim- 19 at low (0.123 bpp) bitrates. The first row shows reconstructions with only one of seven latent modulations sets active at a time. The second visualizes the corresponding raw latents, upsampled to output resolution.
High bpp 1.425
Figure 27: Reconstruction and visualization of latents for kodim- 19 at high (1.425 bpp) bitrates. The first row shows reconstructions with only one seven latent modulations sets active time. The second row visualizes the corresponding raw latents, upsampled to output resolution.
inaccuracies (e.g., object colors) while preserving semantic correctness. This aligns with our C* coding design, which prioritizes accurate object boundaries while allowing coarser approximations for background regions to preserve semantic integrity and reduce artifacts, Subsequently, to refine specific regions, corresponding LSNs (LSN-1) are transmitted as layer-1. 1. The remaining areas inferred jointly from both layers (LSN-0 and LSN-1) 1) through averaging. This process continues with additional LSNS, enabling progressive refinement and extensibility more layers/LSSNs.
More experimental examples To further illustrate the semantic generalization capability for the model trained the Kodak dataset with three regions (Fig. 24 to perform inference across different regions using different LSNs.
layered compression application,
30 we can observe that local INRs can infer semantics beyond their assigned regions. By progressively transmitted L.SN for different regions, it can refine earlier outputs. This behavior comes from the global-loca modulation design: LSNs can capture shared features across regions (c.g., common colors) while encoding contrastive, region-specife details (c.g.. distinct object colors) that are unrecoverable by other LSNs,
Results are visualized in Fig. 28
36

---

Ground truth
Region mask
Layer (gwe)
Layer (gy)
Layer (gwe)
mmm
mm
bpp/PSNR: 0.140/31.54
bpp/PSNR: 0.128/30.41
Figure 28: Visualization of layered compression: The background LSN gwo is first transmitted as layer 0, followed by Iwi for the blue region (layer 1), and finally 9w2 for the red region (layer 2). We can see that colors and textures (e.g., red hat and golden ball) are refined with the additional LSN parameters.
Region
(gwo)
Layer (yy))
Layer (0w=)
bpp/PSNR: 0.118/33.54
hpp/PSNR: 0.074/31.02
bpg/PSNR: 0.170/28.18
Figure 29: Visualization layered compression: The background LSN gwo is first transmitted as blue region (layer 1), and finally gwa for the red region (layer 2).
layer 0, followed by 9w1 for the We can see that specific colors (yellow and green hat / people tower) and textures are refined with the additional LSN parameters.
37

---

truth
Region
Reconstruction
Low rigme
bpp/PSNR: 0.093/32.60
LSNO (d)=) output
LSN1 (8y=) output
LSN2 (#w-) output
Ground truth
Region mask
Reconstruction
Middle bpp rigme
bpp/PSNR: 0.368/38.82
((
LSN1 (4t=) output
LSN2 (0p=) output
Ground
Reglon
Reconstruction
High bpp rigme
bpp/PSNR: 0.742/42.06
LSND (Gge) output
LSN1 (sty-) output
LSN2 (gn²)) output
Figure 30: Visualization of layered compression at various bitrates, where the background LSSN transmitted as layer 0, followed by the blue and red region LSSSs as layers 1 and 2. Shared features (e.g., green color, bird mouth) are captured across regions, while contrastive details (e.g.. bird-specific colors) are refined by region-specific LSNs. At low bpp, inferring context and features from other regions is more challenging: high bpp. richer latent modulations enable better cross- region inference.
38

---

E,5 Experiments for partial decoding
To further illustrate the benefits of partial decoding, we report detailed computation and bit cost savings for surveillance scenario in Table For experimental details, we refer to Fig. 5 in our supplementary materials for a demo illustration. We can observe that MoRIC achieves up to 73.56% and 37.31% bitrate savings compared to VTM and MLIC++, respectively. Thanks to the use of contour information, MoRIC achieves significantly lower decoding complexity in partial decoding scenarios by coding only the target region with simpler neural functions. As shown in Table [1 baseline methods require approximately 2x (VTM) and 1235x (MLIC++) more computation than MoRIC.
Table 11: Bitrate and computational savings enabled by partial decoding in MoRIC.
Method
VTM
MLIC++
MoRIC
PSN
52.301
52.332
52.584
bit cost (10*)
2.107
1.667
1.214
bit saving vs. methods
73.56%
37.31%
Computation saving methods
2 times
1235 times
E.6 Ablation study over model components
To evaluate each component of MoRIC:
C* coding, GMN with PCM, and LSNs, this section presents ablation studies on each component. The results are reported in Table each component contributes to the performance of MoRIC. C" coding is essential for enabling region- wise compression, yielding a 0.447 BD-rate reduction. The PCM module contributes significant -3.56% decrease in BD rate, highlighting its impact on RD performance. Removing the LSN reduces MoRIC to variant of the C3/COOL-CHII series, resulting in RD performance decrease (+5.35% BD-rate), underscoring the importance of modular region-wise design.
Model Variant
BD rate vs. MoRIC
Proposed MoRIC scheme
0.0%
w/o C* coding (rectangular region)
+0.47%
w/o PCM-GMN
+3.56%
w/o LSN
+5.35%
Table 12: Ablation study on different mechanisms for standard full image compression, using an ARM-16 model, where À E {8e- 2e-3 1e-3, ,5e ,3 2,- 24.4.. A higher BD rate indicates worse RD performance.
E.7 Ablation study over artifacts
For region-based coding scheme, the contour boundaries of MoRIC remain barely visible, even low bitrates such as 0.05 bpp (see our visualizations). This robustness stems from two key design choices in MoRIC:
Design of the global modulation network (GMN): MoRIC integrates global-local context through its GMN and progressive modulation, effectively suppressing artifacts. Similar strategies have been shown to reduce artifacts in previous INR literatures 19].
Region-wise fitting strategy: Instead of fitting the image in patch-wise manner, MoRIC performs region-wiss wise fitting, enabled from C* coding. enhancing INR representation while reducing artifacts (as also observed in
To further quantify the effect of artifacts, we include an ablation study on GMN and region-wise fitting (exp-1 and exp-2) for artifacts analysis and quality assessments, reporting PSNR, MS-SSIM.
39

---

PSNR SeiieeeggeSSNR-Smeeeeeee edge in Tables E (two metrics from 19 that assess artifacts via Canny edge detection with disk dilation). For exp-1, compare MoRIC with variant that removes the GMN component, denoted as MoRIC (w/o GMN). Exp-2 replaces the target region of MoRIC with rectangular patch to cover the same target, denoted MoRIC (rect), where contour coding omitted.
Table 13: Ablation study for MoRIC (w/ GMN) for artifacts analysis on Kodak.
Rate
0.15413
0.5399
0.7892
1.2003
BD-rate vs. MoRIC (%)
Observed artifacts Without GMN: Ringing artifacts, gradient discontinuity, inconsistent textures
PSNR
28.910
34.437
36.445
39.057
+7.03
MS-SSIM
11.403
16.788
18.674
21.108
+6.91
PdNRndge
25.038
32.104
34.527
37.604
+6.11
PSNR smooth
31.960
35.628
37.326
39.635
+8.56
Table 14:
Ablation study for MoRIC (rect) for artifacts analysis Kodak.
Rate
0.1500
0.3399
0.7496
1.1157
BD-rate vs. MoRIC (%) 4
Observed artifacts
PSNR
29.067
34.509
36.645
39.317
+2.53
With rec contours: Very visible
MS-SSIM
11.518
16.911
18.857
21.273
+2.28
PSNRadge
25.159
32.122
34.747
37.950
+-2.7
stitching artifacts
amonth
32.171
35.720
37.490
39.817
+.2.02
between patches.
E.8 Ablation study over segmentation errors
We conducted additional experiments by training MoRIC using masks with varying degrees of over- and mnder-segmentation errors. Specifically, we simulate small and substantial segmentation errors via mask dilation and erosion, with IoU values of 14.22% 2322% 34.18% (under-segmentation) and 19.85%/48.50 48.5% (over-segmentation)
Results are shown in the table below. We observe that MoRIC is robust to segmentation imperfections, especially when the segmentation IoU is below 20%. with performance degrading gradually as segmentation quality decreases. However, for both under- and werr-eegmentation. more significant performance drops begin to appear when the IoU approaches 30" 40%. Additionally, substantial segmentation eтrors introduce encoding instability, occasionally leading suboptimal RD performance. While MoRIC does not currently optimize region selection, we believe that better segmentation strategies could yield substantial improvements by leveraging this trade-off.
Table 15: Ablation study over segmentation error for MoRIC on Kodak dataset.
Methods
PSNR (dB) hpp
BD>ratee
MoRIC (lossy coding)
3.95%
20.121/0.1516
34.599/0.55
36.655/0.7449
11.250/1.4533
Under-segmentation
14.22% IoU
29.035/0.1537
34.573/0.55
28.570/0.7663
11.256/1.4600
+2.11
34.18% loU
29.059/0.1550
34.569/0.532)
66.602/0. 76044
41.042/1.50 50788
+2.76
19.85% JoU
29.066/0.155
34.564/0.532
36.624/00 66.624/0.7617
41.235/1. 46.6
+2.09
Over-segmentation
48.58% IoU
29.038/0.1553
34.562/0.5327
36.603/0.759)
41.061/1.5513
+3.29
40


Reviews:
[{"review_id": "sg0KxFyVbu", "reviewer": "Reviewer_Ek8z", "summary": "The proposed MoRIC is a novel INR-based image compression method that represents each region with corresponding shape and texture codes, improving local adaptation and enabling fine-grained rate-distortion control. MoRIC achieves state-of-the-art single-object compression with lower decoding complexity, holds promises for fixed-background scenarios.", "questions": "1. Provide detailed descriptions of the encoding time.\n2. Provide the performance of commercial compressors.\n3/ The necessity of including the results on general natural scenes, since the proposed approach does not have clear advantageous on such data.", "limitations": "yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n1. The rationale behind the proposed approach is inspiring and fits the fixed-background applications well.\n2. The idea of progressive encoding is an attractive feature for INR-based compression, which permits saliency-specific compression.\n\nWeakness\nThe manuscript lacks descriptions and discussions of the cons of the proposed approach, such as\n1. What are the quality, expenses, and criteria of region partitioning? The partitioning might result in non-reasonable over-segmentation / under-segmentation, and the time consumption in partitioning should also be counted in the compression running time. The partitioning can be from a semantic or pixel perspective, which one is favoured?\n2. I expect quantitative figures on the encoding time and the time spent on different modules. \n3. The performance on general natural scenes is not that promising (Fig. 7); the decompression is faster than four competitors. can you explain why? Is it attributed to the region-specific strategy?\n4. I understand that the method is INR-based and might be inferior to conventional commercial coding, such as H. 266, I still expect a comparison with the sota compressors, which is important to evaluate the performance of the proposed approach.", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the valuable feedback. In response, we will: (a) add descriptions of our partitioning strategy and include ablation studies on the impact of segmentation quality; (b) provide a detailed breakdown of coding cost across various regions, along with corresponding theoretical complexity analysis; (c) include additional experiments on general natural scenes (CLIC2020 dataset); and (d) incorporate more baseline comparisons in the revised manuscript.\n\nNext, we address the commented weakness and the questions point by point.\n\n- **W1.** The current MoRIC region partitioning is guided by semantics and based on SAM2 [1]. The reviewer is correct that partitioning may result in unreasonable segmentation. However, MoRIC **does not rely on highly accurate segmentation**, thanks to the robustness of its GMN design and INR fitting capability. In fact, while lossy contour coding may cause minor over-segmentation, the resulting bit savings without significantly sacrificing distortion often lead to slightly improved rate-distortion trade-offs.\n\n    To evaluate this, we conducted experiments assessing the impact of segmentation quality under both over- and under-segmentation scenarios. The results are presented in **Table 4.3** (in our response to **Reviewer [1oDR]**).\n\n    The partitioning time of MoRIC is around 533-830 ms (3090GPU) for Kodak samples, which is reported in **Table 2.1** (in our response to **Reviewer [3Cij]**) as part of the coding cost. Since overfitted codecs are typically encoded offline, this one-time partitioning will have minimal impact on practical deployment.\n\n    In summary, MoRIC favors semantic partitioning over pixel-level precision due to its robustness to contour errors. Experimental results show that this design is both efficient and effective, while also maintaining strong perceptual quality, as demonstrated by the MS-SSIM experiments in **Table 4.2** (in our response to **Reviewer [1oDR]**).\n\n    [1] Ravi, Nikhila, et al. \"SAM 2: Segment Anything in Images and Videos.\" ICLR 2025.\n- **W2.** In addition to Table 4 in the manuscript, we will include a module-wise breakdown of coding time and a theoretical complexity analysis (which is detailed in **Table 2.1** from our response to **Reviewer [3Cij]** due to space limitations) into our manuscript. Specifically, the backward pass complexity is approximated to twice the MACs of the forward pass, following [2].\n\n    [2] Baydin, Atilim Gunes, et al. \"Automatic differentiation in machine learning: a survey.\" *Journal of Machine Learning Research* (2018).\n- **W3. (a) Performance concerns**: We would like to highlight that MoRIC sets a **new state-of-the-art** among overfitted codecs, **outperforming VTM (H.266)** on natural scene datasets such as **Kodak and CLIC2020**, a strength also noted by Reviewers [3Cij], [BiKZ] and [1oDR]. While MoRIC falls short of leading neural codecs like MLIC++ in RD performance, it achieves over 100× lower decoding complexity.\n\n    To further demonstrate its advantages on general natural scenes, we conducted additional experiments on the **CLIC2020 dataset** (as shown in **Tables 1.1, 1.2, and 1.4**), where even more pronounced gains were observed (**approaching MLIC and outperforming ELIC on CLIC2020**). Additionally, we also provide MS-SSIM results for MoRIC (see **Table 4.2** in our response to **Reviewer [1oDR]**), where **MoRIC approaches ELIC on Kodak**. Taken together, these results offer a comprehensive evaluation and underscore the promise of MoRIC, with evidence that is both strong and well-supported.\n\n    Beyond the RD experimental gains, MoRIC introduces broader contributions, including a modulated local-region fitting strategy, a chain-coding paradigm, and faster encoding convergence (see **Table 3.2** in our response to **Reviewer [BiKZ]**). These advances offer independent value for both INR and overfitted codec design. We welcome further suggestions to strengthen the soundness and impact of this work.\n\n**Table 1.1 Detailed RD datapoints of MoRIC on CLIC2020 (professional validation dataset).**\n\n| **Rate (bpp)**   | 0.0852 | 0.1353 | 0.3533 | 0.5140 | 0.7898 | 1.0721 |\n|------------------|--------|--------|--------|--------|--------|--------|\n| **PSNR (dB)**    | 30.6281 | 32.1680 | 35.9424 | 37.5443 | 39.7148 | 41.3063 |\n\n**Table 1.2 Comparison of different schemes for standard full image compression on CLIC2020.**\n\n| **Methods** | MLIC++ | MLIC | CST | EVC (SS/MM/LL) | C3 (fixed/adapt.) | **MoRIC (ours)** |\n|-------------|--------|------|-----|----------------|-------------------|------------------|\n| **BD-rate over VTM-19.1  (%).** | -16.31 | -12.12 | 7.4 | 7.93 / 1.45 / -0.80          | -3.61 / -6.47 |  -3.14 / -6.37 / -8.22 / **-10.58** |\n| **Decoding complexity (MACs/pixel)** | 414k | 447k | 583k | 35k / 124k / 258k     | 2925 |  1378 / 1659 / 1844 / **2882** |\n- **W3. (b) Decoding speed**: MoRIC achieves the **fastest CPU decoding speed** among all methods in Table 4 (object compression) of the manuscript. Specifically, most of the computation in overfitted codecs lies in the entropy model and synthesis module. MoRIC addresses this by two key design choices:\n\n  - **Explicit contour representation:** MoRIC skips the expensive auto-regressive decoding for latents outside target regions.\n  - **Progressive Concatenated Modulation (PCM):** This design enables efficient region-wise reconstruction under lightweight architecture. As a result, the synthesis module requires just **262 MACs/pixel**, which is approximately **81%** of COOL-CHICv4 and **62%** of C3, while still delivering superior RD performance.\n\n    To improve clarity, we will incorporate the paragraphs above, the coding cost analysis (**Table 2.1** (in our response to **Reviewer [3Cij]**)), and the CLIC2020 experiment results (**Table 1.1, 1.2, and 1.4**) into the revised manuscript.\n- **W4.** We would also like to respectfully clarify a possible misunderstanding: we have included both **VTM-19.1** (the reference implementation of **H.266**) and **MLIC++** (current state-of-the-art neural codec) for comparison in our manuscript. And as shown in our experiments, MoRIC **outperforms VTM-19.1 (H.266)** on standard image compression benchmarks such as **Kodak and CLIC2020**. Additionally, in single-object compression, MoRIC **surpasses** MLIC++ while **achieving 100×–1000× lower decoding complexity**. This advantage is particularly significant in high-bpp regimes.\n\n   To address the reviewer’s concern, we will add more baselines (**Table 1.3 and 1.4**) and revise the manuscript to more clearly highlight the baseline choices, as follows:\n\n**Table 1.3 More baselines on Kodak dataset.**\n\n| **Traditional/INR codec** | **JEPG2000** | **HEVC (HM)** | **BPG** | **MSCN** | **VC-INR** | **RECOMBINER** |\n|---------------------------|--------------|---------------|---------|----------|------------|----------------|\n| BD-rate over VTM-19.1     | 95.42%       | 24.90%        | 22.53%  | 115.91%  | 73.71%     | 63.86%         |\n\n| **Autoencoder codec**     | **BMS**      | **MBT**       | **CST** | **WYH**  | **STF**    | **ELIC**       |\n|---------------------------|--------------|---------------|---------|----------|------------|----------------|\n| BD-rate over VTM-19.1     | 30.34%       | 10.85%        | 3.99%   | -0.44%   | -3.96%     | -6.85%         |\n\n**Table 1.4 More baselines on CLIC2020 dataset.**\n\n| **Image codec**     | **BPG** | **ELIC** | **Cheng2020** | **WYH** | **STF** | **CCv4** | **MoRIC (ours)** |\n|---------------------|--------|----------|----------------|--------|--------|--------|------------------|\n| BD-rate over VTM-19.1 | 39.28% | -7.04%   | 7.22%          | -4.77% | -3.22% | -6.58% | -10.58%          |\n\n  “We evaluate MoRIC on the DAVIS, Kodak, and CLIC2020 datasets, comparing it with classical codecs (VTM, the reference implementation of H.266), autoencoder-based neural codecs (EVC for low complexity; MLIC++ for state-of-the-art RD performance), and recent overfitted codecs (C3 and COOL-CHIC v4). Additional baselines are provided in the appendix.”\n\n   “MoRIC surpasses state-of-the-art neural codecs in single-object compression, and outperforms VTM on standard compression benchmarks. These results highlight progress on key challenges in overfitted codecs, including achieving high RD performance with low decoding complexity and faster encoding through region-wise coding.”\n\n**Answers to questions:**\n\n- **Q1.** In our response to W2, we provided a detailed breakdown of both the theoretical and practical coding costs (presented as **Table 2.1** in our response to Reviewer [3Cij]).\n\n- **Q2.** In our response to W4, we incorporated additional baselines (shown in **Tables 1.3 and 1.4**).\n\n- **Q3.** We added experiments on the **CLIC2020** dataset (a standard benchmark with 41 high-resolution images) and included additional MS-SSIM results on Kodak, demonstrating promising performance gains (see **Tables 1.1, 1.2, 1.4, and 4.2**)."}, {"review_id": "9DpoIwcC8a", "reviewer": "Reviewer_3Cij", "summary": "This paper introduces MoRIC, a novel image compression codec based on implicit neural representations (INRs). Unlike prior work that uses a single INR to model the entire image, MoRIC takes a modular, \"divide and conquer\" approach. It partitions an image into multiple, arbitrarily-shaped regions and assigns a dedicated, lightweight Local Synthesis Network (LSN) to compress each one. To ensure coherence across regions and prevent artifacts, a shared Global Modulation Network (GMN) injects global context into each LSN. A key component of this framework is a new adaptive chain coding method, named C* coding, designed to efficiently compress the region contours. The authors demonstrate that MoRIC achieves state-of-the-art rate-distortion performance for single-object and standard image compression among overfitted codecs, while maintaining low decoding complexity.", "questions": "Could you provide more detailed analysis on the trade-off between the number of regions (N) and overall complexity? Specifically, how does the bitrate for contours and network parameters scale with N? Is there an adaptive mechanism that could determine an optimal N for a given image to balance performance and overhead?", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.The proposed modular, region-based paradigm for overfitted INR codecs appears to be a novel contribution. This \"divide and conquer\" strategy is an intuitive way to potentially improve adaptation to local image statistics compared to monolithic models. This design could enable applications like fine-grained rate control and single-object compression.\n2.The paper presents promising experimental results. According to the reported figures, MoRIC seems to achieve a strong rate-distortion performance, setting a new benchmark among overfitted codecs and even surpassing the classical VTM codec on the Kodak dataset. \n\nWeaknesses:\n1.A potential limitation is the method's reliance on manual or semi-manual region selection. While this is understandable for an initial study, it might pose a challenge for practical, fully automated systems. The performance of the codec could be sensitive to how these regions are defined.\n2.The encoding process of the proposed method appears computationally intensive. The paper acknowledges this, and it's a known trade-off for this paradigm. This aspect may confine the method's applicability to specific scenarios where encoding time is not a critical constraint.", "was_revised": true, "final_justification": "The authors' rebuttal has adequately addressed my concerns, and I am inclined to accept this paper.", "rebuttal": "We thank the reviewer for the valuable feedback. In response, we will: (a) include an ablation study on the robustness of partition strategy in MoRIC; (b) introduce an automatic partitioning algorithm with adaptive region count; (c) add experiments demonstrating MoRIC’s encoding advantages over other overfitted codecs; and (d) provide a detailed analysis of the trade-offs between region count, complexity, and bitrate.\n\nNext, we address the commented weakness and the question point by point.\n\n- **W1.** We thank the reviewer for highlighting this important point. While our current implementation uses SAM2 for region selection, we agree that fully automated partitioning is essential for practical deployment.\n\n  To this end, we note that MoRIC **supports automatic region partitioning** via connected component analysis on SAM2 outputs, enabling automatic selection of the top-k object regions. It is also compatible with task-adaptive strategies, including prompt-guided segmentation from SAM2, as well as alternatives like DINOv2 with DeepLabv3 or EML-Net for saliency-based partitioning, allowing enhanced adaptability and partition quality across diverse applications.\n\n  It is worth noting that the performance of MoRIC is **robust to segmentation imperfections**, thanks to its advanced PCM design and region-wise INR fitting, as demonstrated in our response to **Reviewer [1oDR] (Table 4.3)**.\n\n  We will add the following clarification to the revised manuscript:  \n  *“MoRIC is robust to segmentation quality, supports automatic region partitioning via SAM2, and can incorporate task-adaptive strategies such as prompt-guided or saliency-aware segmentation to enhance partition quality and compression performance.”*\n- **W2.** High encoding complexity is a common phenomenon across **all overfitted coding paradigms** due to their instance-specific optimization, and is not unique to MoRIC. Potential solutions include meta-learning [1] and engineering optimizations [2], which have been shown to accelerate encoding by 10×–100×, reducing Kodak sample encoding time to around 20 seconds.\n\n  In this context, we would like to highlight another contribution of our work (previously discussed in Supplementary Section 3.1): **MoRIC mitigates encoding complexity to some extent** via a region-wise fitting strategy with shared modulation, which accelerates convergence and improves practical efficiency.\n\n  This design **significantly reduces** the number of required **encoding steps** compared to prior overfitted codecs, achieving a **2–3× algorithmic speedup** (see **Table 3.2** in our response to **Reviewer [BiKZ]**). These convergence gains, combined with potential engineering improvements, represent meaningful progress toward practical, low-latency overfitted codecs.\n\n  [1] Dupont, Emilien, et al. \"COIN++: Neural Compression Across Modalities.\" *Transactions on Machine Learning Research*.\n\n  [2] Blard, Théophile, et al. \"Overfitted image coding at reduced complexity.\" *2024 EUSIPCO*.\n\n**Answers to questions:**\n\n- **Q1.** Following reviewer's suggestion, we provide a detailed analysis of the trade-off between region count (N) and coding complexity. As shown in **Table 2.1**, the breakdown of coding cost is reported for various values of N (1–3). (Considering various existing implementations of entropy coding schemes and for fair comparison with [3], we exclude range coding time from our measurements, which is also a component of every classical codec.)\n\n    [3] Kim, Hyunjik, et al. \"C3: High-performance and low-complexity neural compression from a single image or video.\" CVPR. 2024.\n\n**Table 2.1 Encoding (1000 steps) and decoding cost breakdown of MoRIC on Kodak dataset for different numbers of regions.**\n\n_SAM2 partition time: 533–830 ms (GPU); C* encoding: 119.58 ms (CPU); C* decoding: 12.86 ms (CPU)_\n| MoRIC (N=1 region) | **Module**| **ARM**| **GMN**| **LSN1**| **LSN2** | **LSN3** |\n|-|-|-|-|-|-|-|\n|| GPU encoding time (s/1k steps)  | 7.382  (29.89%)| 12.331 (49.93%)   | 4.984 (20.18%) | – | – |\n|| Encoding complexity kMACs/pixel   | 2175| 2589| 99| – | – |\n|| CPU decoding time (ms) | 182.17 (53.03%)  | 153.35 (44.64%)   | 8.03 (2.34%)  | – | – |\n|| Decoding complexity MACs/pixel    | 725 | 863 | 33 | – | – |\n\n| MoRIC (N=2 regions) | **Module**| **ARM**| **GMN**| **LSN1**| **LSN2**| **LSN3**|\n|-|-|-|-|-|-|-|\n|| GPU encoding time (s/1k steps) | 7.279 (27.56%) | 13.298 (50.35%)| 2.878 (10.90%)| 2.956 (11.19%)|–|\n|| Encoding complexity kMACs/pixel| 2175 | 3381| 99 | 99 |–|\n|| CPU decoding time (ms)| 182.85 (44.71%)  | 209.45 (51.21%)   | 8.05 (1.97%) | 8.62 (2.11%)|–|\n|| Decoding complexity MACs/pixel|725|1127| 33| 33|–|\n\n| MoRIC (N=3 regions) | **Module** | **ARM**| **GMN**|**LSN1**|**LSN2**|**LSN3**|\n|-|-|-|-|-|-|-|\n|| GPU encoding time (s/1k steps) | 6.961 (21.71%)   | 15.512 (48.38%)| 2.960 (9.23%) | 2.703 (8.43%) | 3.926 (12.25%)|\n|| Encoding complexity kMACs/pixel  | 2175| 4173  | 99 | 99  | 99 |\n|| CPU decoding time (ms)| 185.28 (38.09%)  | 275.57 (56.65%) | 8.39 (1.72%)| 8.10 (1.67%) | 9.14 (1.88%)|\n|| Decoding complexity MACs/pixel   | 725| 1391 | 33 | 33 | 33 |\n\nFrom the table, we observe that increasing the number of regions leads only to a slight rise in overall complexity. Specifically, each additional local INR adds 33 MACs/pixel from LSNs and 264 MACs/pixel from GMN in the forward pass. The added cost primarily arises from extra operations in the shared modulator to accommodate more local INRs (see Fig. 5 in our manuscript).\n\nWe also recognize the importance of real-world latency and thereby include a breakdown of actual coding time across regions to provide practical insights. Here the time for the partition and contour coding is also provided. From our experiments, ARM exhibits consistent time costs across different region settings. Each additional LSN adds approximately $8$–$9$ ms to decoding time and $2$–$4$ seconds for 1000 encoding steps. A similar trend is observed for GMN, which dominates the total coding time and increases significantly as the number of regions grows, consistent with its complexity analysis. Note that all reported results are based on the same unoptimized code, with decoding executed serially. Significant speedups are expected for MoRIC with proper engineering optimizations.\n\nOverall, MoRIC demonstrates strong scalability with respect to region count, as the added complexity and latency remain acceptable relative to its strong rate-distortion performance. We will include the above discussion and **Table 2.1** in the revised manuscript to provide a more comprehensive analysis of complexity and coding time across different region numbers.\n- **Q2.** We repeat the experiments from Fig. 9 in the manuscript and provide a detailed breakdown of the bitrate share between contours, network parameters, and latent for different rate regimes and region numbers $N$ (see **Table 2.2**). \n\n  From the table, we can observe that C* coding can compress contours with minimal bitrate overhead, remaining as low as 1.89% for $N=2$ and increasing only slightly with more regions (up to 3.20% for $N=3$). As bitrate increases, the relative impact of contour cost becomes negligible, allowing MoRIC to achieve competitive RD performance with finer region partitioning efficiently.\n\n  We will include the above discussion and **Table 2.2** in the revised manuscript to provide a more comprehensive analysis of bitrate distribution across different compression rates and region numbers.  \n\n**Table 2.2 Bit rate breakdown for MoRIC across region numbers on Kodak dataset.**\n\n| **Bit cost share**| **Low bpp** | **Medium bpp** | **High bpp** | **BD-rate vs. MoRIC (single)** |\n|-|-|-|-|-|\n| **MoRIC (single region)**  | 0.11815 | 0.41885  | 1.27234 | 0 |\n| Contour/Parameters/Latent (%) | 0% / 25.39% / 74.61% | 0% / 8.14% / 91.86% | 0% / 2.89% / 97.11% |                                |\n| **MoRIC (N=2 regions)**  | 0.11940 | 0.41879 | 1.24859 | -1.29% |\n| Contour/Parameters/Latent (%) | 1.89% / 26.01% / 72.09% | 0.54% / 8.41% / 91.05% | 0.18% / 3.11% / 96.71% |                                |\n| **MoRIC (N=3 regions)**  | 0.12067| 0.41567| 1.24135| -1.72%|\n| Contour/Parameters/Latent (%) | 3.20% / 26.71% / 70.08% | 0.93% / 8.55% / 90.52% | 0.31% / 3.22% / 96.47% |                                |\n- **Q3.** There exist adaptive strategies for determining the number of regions and corresponding partitions for MoRIC. In general, images with substantial regional variation benefit from using more local INRs, which enables faster fitting and improved compression performance.\n\n  This observation suggests that the problem of getting the adaptive region number can be transformed into an analysis of the complexity of an image’s regional distribution. While a full investigation of how region distribution variation impacts partitioning and corresponding RD performance is beyond the scope of this paper, we consider this a valuable suggestion and a promising direction for future development of implicit codecs. To this end, we outline two practical solutions:\n\n  (a) **Feature-driven region partitioning**: Leverage a strong backbone such as DINOv2 for robust region-feature extraction and semantic grouping, followed by SAM2 to perform region segmentation guided by these cues. This combination enables adaptive region partitioning that captures region-wise semantic structure, where more complex images naturally result in more regions guided by semantic grouping.\n\n  (b) **Saliency-guided region partitioning**: A learning-based saliency model such as EML-Net can be used to guide partitioning by grouping visually important or semantically similar areas. Subsequent posterior analysis and filtering can further refine the selection to balance coding complexity and rate-distortion performance.\n\n  These approaches demonstrate MoRIC’s versatility and strong potential for integration with emerging methods and diverse application scenarios."}, {"review_id": "Qk7IFzRUTB", "reviewer": "Reviewer_BiKZ", "summary": "This paper introduced MoRIC, an image compression model based on implicit neural representations. MoRIC features region-based model fitting, i.e., instead of fitting a single model to every pixels, MoRIC assign different models to different regions, such that the models can better fit the local distributions. To achieve region-based coding, MoRIC extract the contours and apply chain coding, enabling coding with arbitrary shape regions, while maintaining high coding efficiency.", "questions": "- For evaluation with the single-object compression, do you compute the average over all pixels (including the masked pixels)?\n- How are the baseline models being evaluated with the single object cases? Do you overfit the INR based codecs for the masked pixels as well?\n- Is coding the contour more efficient than coding masks (with a high efficient codec)?\n- Does the reported encoding/decoding time including everything, both of the entropy coding/decoding time/contour generation & compression?\n- Why using DAVIS dataset? It isn’t a standard dataset for image compression. Also, in this dataset, the objects could only occupy very small part of the images, which the proposed method could have a larger advantage with the single object case.\n- How were the ablation study models being built? Are the modules simply being removed? Did the models be adjusted for fixing the complexity & number of parameters?", "limitations": "yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths\n- The idea of applying region-based synthesis networks is novel and rational. In images, there are clearly different local distributions which fitting different synthesis networks can benefit the coding.\n- Open sourcing the C* coding is an important contribution.\n- The results of both single object/full image compression are promising.\n\nWeaknesses\n- The practical application of scalable layered compression has not been discussed. The proposed model still requires decoding the latent, plus computing the full shared components ($f_{\\theta}$), even if the target is only part of the scene. The partially decoded image is not a low quality version of the original image, but an incorrect colour version of it. Also, progressively decode different regions also require caching the shared features/variables. The authors should consider discussing what is the advantage of decoding only part of the image (e.g. saving how many computation?).\n- The region selection requires manually selecting, when the mask is not provided. This is not practical in most of the image compression applications.\n- While the theoretical complexity is low, the performance/actual coding trade-off has not been evaluated. It is not clear if the improved performance worth the slow down of coding.", "was_revised": true, "final_justification": "A new image coding model is proposed in this paper with region/layered compression based on INRs. This is an important but yet to be explored topic. The codec performance is promising, although it performance is not groundbreaking in the general image compression task, but it supports layered coding which will could better serve certain applications. The evaluation and experiments are comprehensive, especially considering the additional details provided during rebuttal/discussion. The concerns raised have all been addressed. Overall, I think this is a technically solid paper.", "rebuttal": "We thank the reviewer for their valuable feedback. In response, we will:  \n(a) include a discussion on practical applications for scalable layered compression;  \n(b) discuss automatic partitioning alternatives;  \n(c) add experiments analyzing the trade-off between performance and coding cost;  \n(d) add experiments to validate the efficiency of C\\* coding; and  \n(e) include additional experiments on the CLIC2020 dataset.\n\nNext, we address the identified weakness and the questions point by point.\n\n- **W1.** To highlight scalable layered compression applications of MoRIC, we have revised the manuscript to include the following section:\n\n  \"MoRIC supports progressive rate control with semantic consistency, enabling several practical applications:\n\n   (i) **Goal-oriented progressive compression**: Suited for scenarios like surveillance and edge AI, where full-resolution reconstruction is not always needed. Semantic outlines are sent first, with key regions refined on demand, saving bandwidth while preserving critical information.\n\n    (ii) **Distributed compression**: In multi-agent settings (e.g., robotics, NeRF), agents transmit only observed regions; others are inferred or selectively refined in a MoRIC fashion. \n\n  (iii) **Interactive content delivery (e.g., VR, AR, games)**: Decoding adapts online to user attention, delivering high-quality reconstruction in focus areas, while other regions are inferred and progressively refined as attention shifts.\n\n  (iv) **Video streaming/preview**: Coarse frames with accurate key regions and semantically consistent background are transmitted first, followed by progressive refinement for a seamless viewing experience.\"\n\n  To further illustrate the benefits of partial decoding, we report detailed **computation and bit cost savings** for a surveillance scenario in **Table 3.1**. For experimental details, we refer to Fig. 5 in our supplementary materials for a demo illustration. \n  \n  MoRIC achieves up to 73.56% and 37.31% bitrate savings compared to VTM and MLIC++, respectively. It also provides substantial computational savings, thanks to its low decoding complexity, where the complexity of VVC is estimated to be comparable on standard hardware.\n\n**Table 3.1. Bitrate and computational savings enabled by partial decoding in MoRIC**\n\n| **Method** | **VTM** | **MLIC++** | **MoRIC** |\n|-----------|--------|-----------|----------|\n| **PSNR (dB)** | 52.301 | 52.332 | 52.584 |\n| **Bit cost (×10⁴)** | 2.107 | 1.667 | 1.214 |\n| **Bit saving vs. methods** | 73.56% | 37.31% | - |\n| **Computation saving** | 2× | 123× | - |\n\n- **W2.** We currently use SAM2 for region partitioning, which inherently supports automatic segmentation and can be extended with other advanced strategies such as saliency-based or prompt-guided segmentation for various compression scenarios. For alternative partition methods, we refer to our response to **reviewer [3Cij] (W1. and Q3)**. For robustness to segmentation quality, we refer to **Table 4.3**.\n\n- **W3.** In response to the comment, we include an experiment evaluating the performance–coding cost trade-off. We train MoRIC (lossy-fixed) and CoolChic-V4 on the Kodak dataset under encoding steps from 1k to 80k. The resulting BD-rates over VTM-19.1 are shown in **Table 3.2**. MoRIC achieves comparable RD performance with 2–3× fewer coding steps, attributed to its region-wise coding strategy, similar to the observations in [1,2].\n\n  Consequently, MoRIC can instead **potentially accelerate convergence** rather than slowing encoding. As shown in Table 3 and Fig. 3 in the supplementary, increasing the number of regions (from 1 to 3) can further improve convergence through more effective INR specialization.\n\n  Previously, encoding cost was typically addressed via engineering optimizations for an overfitted codec. In this context, a 2–3× algorithmic acceleration represents a meaningful step toward practical, low-latency compression. While our results reflect theoretical gains in convergence and complexity, actual latency also depends on deployment factors such as memory and hardware, where further improvements are expected.\n\n  [1] \"Partition speeds up learning implicit neural representations based on exponential-increase hypothesis\", 2023.  \n  [2] Coordx: Accelerating implicit neural representation with a split MLP architecture, 2022.\n\n  In addition to gains in performance, acceleration, and convergence, MoRIC also enables applications such as efficient target-area compression and layered compression. Together, these results demonstrate the effectiveness of the MoRIC design.\n\n**Table 3.2. BD-rate over VTM-19.1 for different schemes across various encoding steps**\n\n| **Encoding steps** | 1,000  | 2,000  | 3,000  | 5,000  | 10,000 | 20,000 | 30,000 | 50,000 | 80,000 |\n|--------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n| **RD of MoRIC**    | 74.36% | 43.17% | 30.71% | 20.60% | 11.27% | 5.82%  | 3.61%  | 1.25%  | -0.91% |\n| **RD of CC-V4**    | 216.16%| 98.16% | 61.53% | 37.33% | 21.22% | 13.42% | 10.49% | 8.62%  | 6.59%  |\n\n**Answers to questions:**\n\n- **Q1.** For the evaluation of the single-object compression task, only the target region is considered, with masked pixels excluded from computation. We will clarify this in the revised manuscript.\n\n- **Q2.** We explored multiple design choices and adopted the best-performing configurations. By default, each baseline codec operates on the smallest rectangular region enclosing the target object, with masked pixels within this region jointly learned. For INR-based methods, we also evaluate variants combined with our proposed C\\* coding algorithm for ablation studies on the architectural innovations. For more details of the baseline models for single-object cases, we refer to Section E.2 of the appendix (Lines 638–655).\n\n**Table 3.3. Contour coding efficiency on Kodak dataset (kodim23), evaluated by error rate / bit cost**\n\n|          Methods                      |   error rate  | /  bit cost     |        |\n|--------------------------------|--------|--------|--------|\n| **Lossless chain coding**      |0% / 1641 |\n| **Quality values of VTM**      | 10     | 36     | 56     |\n| **Performance of VTM**         | 0% / 9128 | 1.48% / 6864 | 6.62% / 1960 |\n| **Step length of C\\***         | 5      | 10     | 15     |\n| **Performance of C\\***         | 0.66% / 890 | 1.17% / 360 | 2.08% / 251 |\n\n- **Q3.** In response, we provide both theoretical analysis and experiments (**Table 3.3**) to support and verify our findings.\n\n  Whether contour coding is more efficient than mask-based encoding depends on the applications. When the goal is to only localize and compress object boundaries, chain coding can offer significant advantages (see **Table 3.3** as an example). Mask-based approaches typically require one bit per pixel across the entire image, whereas contour representations involve a significantly smaller set of pixels. Instead, a basic chain coding scheme can encode directional steps (e.g., 8 directions) using just 3 bits per step. More advanced methods that incorporate geometric cues and relative motion (such as VCC, 3OT, or NAD) can further enhance compression efficiency. These techniques are all included as open-source resources in our supplementary materials.\n\n  As shown in **Table 3.3**, our C\\* coding method achieves lossless compression (error rate 0%) with a comparable bit cost to VTM’s mask coding (with an error rate of 6.62%). Moreover, by adjusting the step length, C\\* coding can further reduce the bitrate with only minimal degradation in coding accuracy.\n\n  However, chain coding may be less efficient in scenarios with very noisy or highly irregular contours, where frequent direction changes and large curvature variations reduce coding efficiency. In such cases, mask-based approaches, especially those leveraging learned priors, can offer greater robustness.\n\n  In our setting, contour coding aligns naturally with the design of overfitted codecs and can be integrated seamlessly into the framework.\n\n- **Q4.** We have now reported a breakdown of the coding cost (**Table 2.1** of our response to **Reviewer [3Cij]**), including all components except range coding time, to ensure a fair comparison with C3. We will clarify this point in the revised manuscript.\n\n- **Q5.** We use the DAVIS dataset because it provides region-level ground truth, which aligns well with our experimental setup. Instead, standard compression datasets typically lack such annotations. Within our MoRIC framework, all region partitions are generated using SAM, and DAVIS allows us to validate our method on high-resolution data with reliable region labels. Additionally, we now include new experiments on the **CLIC2020 dataset** to further assess MoRIC’s performance (see **Tables 1.1, 1.2, and 1.4** in response to **Reviewer [Ek8z]**).\n\n  For small-object cases, baseline methods also benefit from reduced fitting regions (a smaller rectangular), while the relative parameter cost of the INR in MoRIC becomes more pronounced. Intuitively, MoRIC offers greater advantages in scenarios with complex object contours, where its explicit contour-based coding provides more substantial benefits.\n\n- **Q6.** For the ablation study in Table 7, modules are directly removed to assess their individual contributions, without adjusting for complexity or parameter count. We want to note that ensuring strict fairness in parameter count for overfitted codec is challenging, as additional parameters may introduce overhead and can sometimes even degrade RD performance. Here, we focus on validating the impact of the C coding scheme, PCM modulation, and LSN design, to assess whether introducing these mechanisms leads to improved RD performance."}, {"review_id": "7sP9Yfftkz", "reviewer": "Reviewer_1oDR", "summary": "The paper proposes MoRIC, an implicit image compression method consisting of multiple (N=3 is the default) local compressors, each optimized for a specific image sub region specified by a contour. The method is evaluated on 2 datasets for image compression single-object compression. The method achieves SotA in single-object compression for bpp>0.5 and good performance in image compression.", "questions": "- The lossy contour compression approximates the contour with a polygon, did I understand this correctly? If so, I would add a sentence somewhere explicitly stating this, the whole section reads a bit too abstract.\n- Are contour boundaries very visible? I looked at the full image compression examples in the appendix but the images are too small. I would recommend adding an example for very low bitrate that shows what kind of boundary artifacts can be expected\n-  Since in an actual application the GT masks might not be available it would be interesting what the effect of incorrect segmentation masks is on the overall performance. Did you look into this?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The paper is well written and contains multiple well designed figures\n- The method contains multiple novel ideas, such as contour compression, using different networks for different regions and the global modulation network, a network with shared weights among different regions that processes the latent and helps incorporate global information\n- The experiments are very extensive, comparing to multiple SotA methods and an ablation study\n\n**Weaknesses:**\n- For the contour GT information was used (for Davis) and for Kodak the contours were \"manually selected\"(?). In a real compression setting GT masking information can not be expected making this a purely academic method.\n- The model is still outperformed by MLIC++ in image compression and even for single-object compression for low bpp (<0.5)\n- While the decoding complexity is lower than other learned codecs the decoding time (which is practically often the more important metric) is higher (see tab. 6)\n- Davis is somewhat of a non-standard choice for benchmarking, which might make it more difficult to compare the method to other methods in the future. CLIC is mentioned in the supplements but the results are neither in the main paper nor in the supplements?", "was_revised": true, "final_justification": "The paper presents an interesting approach to region based compression. It is well written and evaluated and performs well. The additional evaluations on CLIC, a common compression dataset together with the analysis of the impact of minor segmentation errors made me raise my score to \"accept\".", "rebuttal": "We thank the reviewer for their valuable feedback. Here is our point-to-point response:\n\n**Response to each weakness:**\n\n- **W1.** We currently use SAM2 for region partitioning, which **inherently supports automatic segmentation** and can be extended with other advanced strategies such as saliency-based or prompt-guided segmentation for various applications. For alternative partition methods, we refer the reviewer to our **response to [3Cij]** (W1. and Q3.)\n\n- **W2.** The reviewer is correct. We also want to note that while MoRIC falls short of the MLIC++ in RD performance for standard image compression, it achieves over 100× lower decoding complexity. The superior performance of MLIC++ in the low-bpp regime for single-object scenarios can be attributed to its natural advantage in this setting. In contrast, overfitted codecs face inherent limitations due to the dominance of parameter cost in this regime.  \n\n  In response to this comment, we have added the following clarification in the revised manuscript: \"Although MoRIC shows significant RD gains, it still shares the common low-bpp performance bottleneck with other overfitted codecs due to dominant parameter cost, a challenge that Bayesian INR parameter [1] coding may help address.\"\n\n   [1] He, Jiajun, et al. \"RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations.\"\n\n- **W3.** We thank the reviewers for pointing out this issue. While MoRIC has lower theoretical decoding complexity, its observed latency remains slightly high due to the lack of engineering-level optimizations. We want to note that real-world latency is affected by many uncontrollable factors in a lab setting and can be significantly reduced through various optimization techniques. For example, [2] reports 100 ms decoding time for COOL-CHIC using a C API and binary arithmetic coding, whereas our implementation runs without such optimizations. Notably, MoRIC is implemented with PyTorch serial inference across all modules for research purposes, where substantial speedups are expected with appropriate engineering optimizations.\n\n  To improve clarity over latency, we have added the following clarification to the revised manuscript: \"We want to note that all reported MoRIC results are based on unoptimized research code. Notably, our decoding modules are now executed serially during latency evaluation; a simple parallel execution can substantially reduce runtime. We also expect further improvements through advanced engineering optimizations such as C-API integration and binary arithmetic coding [2].\"\n\n  [2] Blard, Théophile, et al. \"Overfitted image coding at reduced complexity.\"\n\n- **W4.** Due to computational constraints, initial CLIC2020 results were provided in our supplementary materials (Table 1). We have since conducted comprehensive experiments with more RD values and adaptive architectures. (see **Table 1.1, 1.2, and 1.4** in our response to **[Ek8z]**.)\n\n**Response to each question:**\n\n- **Q1.** The reviewer is correct. We will revise the manuscript to include the following additional sentence: \"C* coding approximates object contours using polygonal chains. Starting from an initial point, each contour segment is encoded by a fixed step length and a quantized offset angle relative to the previous direction. A move-to-front transform is applied to the angle sequence, alongside adaptive mechanisms such as global resets, offset adaptation, and contour dilation, to enhance compression efficiency.\" Experiments about the chain-coding are also provided in **Table 3.3** in our response to **[BiKZ]**.\n\n- **Q2.** The contour boundaries remain barely visible, even at low bitrates such as 0.05 bpp. This robustness stems from two key design choices in MoRIC:\n\n  (a). **Design of the global modulation network (GMN):** MoRIC integrates global-local context through its GMN and progressive modulation, effectively suppressing artifacts. Similar strategies have been shown to reduce artifacts in INR literature [3–4].\n\n  (b). **Region-wise fitting strategy:** Instead of fitting the image in a patch-wise manner, MoRIC performs region-wise fitting, enabled from C* coding, enhancing INR representation while reducing artifacts (as also observed in [3]). \n\n  Following the suggestion, we will add visualizations to show artifact suppression, especially at low BPPs. To further quantify this in the discussion period, we include an ablation study on GMN and region-wise fitting (exp-1 and exp-2) for artifacts analysis and quality assessments, reporting PSNR, MS-SSIM, PSNR-edge/PSNR-smooth edge (two metrics from [4] that assess artifacts via Canny edge detection with disk dilation). For exp-1, we compare MoRIC with a variant that removes the GMN component, denoted as MoRIC (w/o GMN).  Exp-2 replaces the target region of MoRIC with a rectangular patch to cover the same target, denoted as MoRIC (rect), where contour coding is omitted. Detailed performance with BD-rate increase for each variant of MoRIC is presented in **Table 4.1**.\n\n**Table 4.1-a  Ablation study for MoRIC (w/o GMN) for artifacts analysis on Kodak.**\n\n| **Rate**         | 0.1543  | 0.5399  | 0.7892  | 1.2003  | BD-rate | **Observed artifacts**         |\n|-|-|-|-|-|-|--|\n| **PSNR**   | 28.910  | 34.437  | 36.445  | 39.057  | +7.03| Ringing artifacts,             |\n| **MS-SSIM**      | 11.403  | 16.788  | 18.674  | 21.108  | +6.91   | Gradient discontinuity,        |\n| **PSNR_edge**    | 25.038  | 32.104  | 34.527  | 37.604  | +6.11 | Inconsistent textures          |\n| **PSNR_smooth**  | 31.960  | 35.628  | 37.326  | 39.635  | +8.56 |  |\n\n**Table 4.1-b Ablation study for MoRIC (rect) for artifacts analysis on Kodak dataset.**\n\n| **Rate**         | 0.1500  | 0.5399  | 0.7496  | 1.1157  | BD-rate | **Observed artifacts**         |\n|------------------|---------|---------|---------|---------|------------------------------|--------------------------------|\n| **PSNR**         | 29.067  | 34.509  | 36.645  | 39.317  | +2.53                        | Very visible                   |\n| **MS-SSIM**      | 11.518  | 16.911  | 18.857  | 21.273  | +2.28                        | Stitching artifacts            |\n| **PSNR_edge**    | 25.159  | 32.122  | 34.747  | 37.950  | +2.87                        | Between patches.               |\n| **PSNR_smooth**  | 32.171  | 35.720  | 37.490  | 39.817  | +2.02                        |                                |\n\nFrom Exp-1, we conclude the importance of GMN: without it, ringing artifacts and inconsistent texture scale can be observed. From Exp-2, we can observe noticeable stitching artifacts in MoRIC (rect) with reduced RD and perceptual performance, highlighting the effectiveness of the C* coding. To further assess MoRIC’s perceptual quality, we report MS-SSIM results under MS-SSIM-trained settings (**Table 4.2**). MoRIC achieves impressive performance, empowered by the above two design choices, closely matching advanced codecs like ELIC. Both **Table 4.1 and Table 4.2** results will be incorporated into the revised manuscript. \n\n[3] Ashkenazi, Maor, and Eran Treister. *\"Towards croppable implicit neural representations.\"\n\n[4] Feng, Haoan, et al. *\"SASNet: Spatially-Adaptive Sinusoidal Neural Networks.\"\n\n**Table 4.2: Detailed MS-SSIM / bpp performance on Kodak dataset.**\n\n| Codec     | Rate 1         | Rate 2         | Rate 3         | Rate 4         | Rate 5         | BD-rate vs. VTM (%) |\n|-|-|-|-|-|-|-|\n| VTM       | 11.963 / 0.1556 | 14.315 / 0.2871 | 16.751 / 0.4920 | 17.961 / 0.6276 | 20.303 / 0.9728 | 0|\n| MoRIC     | 13.910 / 0.1565 | 16.840 / 0.2782 | 19.607 / 0.4801 | 20.605 / 0.5953 | 22.802 / 0.8653 | -43.66 |\n| ELIC      | 12.229 / 0.0907 | 15.863 / 0.2154 | 18.830 / 0.3937 | -| 21.674 / 0.6669 | -46.94  |\n| MLIC++    | 13.299 / 0.0946 | 16.546 / 0.2115 | 18.177 / 0.3012 | 19.808 / 0.4372 | 21.432 / 0.6007 | -54.73 |\n\n- **Q3.** Following the reviewer’s suggestion, we conducted additional experiments by training MoRIC using masks with varying degrees of over- and under-segmentation errors. \n    \n  Specifically, we simulate small and substantial segmentation errors via mask dilation and erosion, with IoU values of 14.22\\%/34.18\\% (under-segmentation) and 19.85\\%/48.58\\% (over-segmentation). Results are shown in **Table 4.3**.\n\n  We observe that MoRIC is robust to segmentation imperfections, especially when the segmentation IoU is below 20%, with performance degrading gradually as segmentation quality decreases. However, for both under- and over-segmentation, more significant performance drops begin to appear when the IoU approaches 30–40%. Additionally, substantial segmentation errors can introduce encoding instability, occasionally leading to suboptimal RD performance.\n\n  While MoRIC **does not currently optimize region selection**, we believe that better segmentation strategies could yield substantial improvements by leveraging this trade-off.\n\n**Table 4.3 Ablation study over segmentation error for MoRIC on Kodak dataset.**\n\n| Methods                     | IoU               | PSNR/bpp (1)         | PSNR/bpp (2)         | PSNR/bpp (3)         | PSNR/bpp (4)         | BD-rate |\n|-|-|-|-|-|-|-|\n| MoRIC (lossy C* coding)    | 3.95%             | 29.121 / 0.1516      | 34.599 / 0.5279      | 36.655 / 0.7449      | 41.259 / 1.4533      | 0       |\n| **Under-segmentation**     | 14.22%            | 29.035 / 0.1537      | 34.573 / 0.5293      | 36.570 / 0.7664      | 41.256 / 1.4609      | +2.11   |\n|                            | 34.18%            | 29.059 / 0.1530      | 34.569 / 0.5323      | 36.602 / 0.7604      | 41.042 / 1.5078      | +2.76   |\n| **Over-segmentation**      | 19.85%            | 29.066 / 0.1541      | 34.564 / 0.5327      | 36.624 / 0.7617      | 41.235 / 1.4666      | +2.09   |\n|                            | 48.58%            | 29.038 / 0.1553      | 34.562 / 0.5327      | 36.603 / 0.7591      | 41.064 / 1.5513      | +3.29   |"}]

Author rebuttal:

Meta-review: This paper introduces MoRIC, an implicit neural image codec which partitions an image into regions and compress each region with local synthesis networks. Key technical components are the global modulator and the contour coding scheme. Overall, the reviewers agreed that the proposed framework is new and reasonable approach that achieves strong empirical results. There has been some concerns, including the limited scope of evaluation (DAVIS and Kodak), high encoding cost, and semi-manual nature of the algorithm. During the rebuttal period, most concerns have been addressed carefully by the authors (including experiments on CLIC), which are mostly acknowledged by the reviewers. I recommend acceptance.
Decision: Accept (poster)