CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting

Linfeng Ye; Zhixiang Chi; Shayan Mohajer Hamidi; En-hui Yang; Konstantinos N. Plataniotis

Figure 1: Panel (a) illustrates that Instant-NGP factorizes an implicit neural representation into a multiresolution hash encoding and a lightweight MLP decoder. A query coordinate is interpolated within each grid level. The resulting per-level features are concatenated. The decoder is trained by minimizing the reconstruction distortion

D(\mathbf{y}_{m},\hat{\mathbf{y}}_{m})

. Panel (b) shows that after training an Instant-NGP model with a 5-level hash grid, we isolate the contribution of each level by retaining only the target level. All other levels’ hash-table entries are replaced with their mean feature value. The resulting reconstructions demonstrate clear spectral stratification. Lower-resolution levels recover smooth, low-frequency structures. Higher-resolution levels progressively contribute fine, high-frequency components. This behavior is quantified by the information density

\mathcal{I}_{f}

, defined in Equation 7 , and plotted against frequency. Vertical dashed lines indicate the sampling frequency of each feature grid level. This confirms that different hash-grid levels encode information from different frequency bands.

Figure 2: Method overview. Panel (a): different images have different information density

\mathfrak{I}(f)

, defined in Equation 7 , for two Kodak images, showing that different images concentrate information at different frequency ranges; the vertical dashed lines indicate the frequency cutoffs implied by the fixed Instant-NGP schedule (gray) versus our collision-aware resolution schedule (blue), which aims to equalize the information being encoded by each level. Panel (b): pixel shuffling to mitigate collision-induced information loss. We partition the image into non-overlapping patches, then shuffle them into channels, thereby reducing the hash collision.

Figure 3: Qualitative comparison on the Kodak dataset. By selecting per-level resolutions (rather than using a fixed, data-agnostic schedule), our method better preserves high-frequency structures and textures, yielding sharper reconstructions than I-NGP and MetricGrid. (Best viewed digitally with zoom).

Method	WIRE [ 32 ]	SIREN [ 38 ]	SCONE [ 22 ]	I-NGP [ 28 ]	NFFB [ 48 ]	NeuRBF [ 6 ]	MetricGrid [ 46 ]	Ours
Rep.	Implicit	Implicit	Implicit	Hybrid	Hybrid	Hybrid	Hybrid	Hybrid
Params (K)	373	207	207	206	208	207	207	205
PSNR $\uparrow$	37.59	38.70	39.72	37.06	38.77	38.70	39.73	40.03
SSIM $\uparrow$	0.9596	0.9512	0.9662	0.9386	0.9537	0.9488	0.9568	0.9714

Table 1: Image fitting results on the Kodak dataset. All methods are trained with the same number of iterations and a comparable number of parameters. Our method achieves the highest PSNR and SSIM while requiring fewer parameters compared to all other methods. Bold and underlined values denote the best and second-best results.

Method	I-NGP [ 28 ]	NeuRBF [ 6 ]	Gaussian Splatting [ 18 ]	GaussianImage [ 58 ]	MetricGrid [ 46 ]		Ours
Rep.	Hybrid	Hybrid	Explicit	Explicit	Hybrid		Hybrid
Params (K)	300	337	3540	560	335	533	341	471
PSNR $\uparrow$	43.88	43.78	43.69	44.08	44.51	45.77	46.24	48.00
SSIM $\uparrow$	0.9976	0.9964	0.9991	0.9985	0.9778	0.9897	0.9906	0.9987

Table 2: Quantitative results of image fitting on the Kodak dataset. Comparing our method against the Gaussian primitive-based approach. Bold and underlined values denote the best and second-best results, respectively.

Figure 4: Gigapixel Image Fitting Performance. Top: Gigapixel images (Tokyo, Pluto, and Girl) with magnified crops highlighting fine-grained details. (Best viewed digitally with zoom). Bottom: Quantitative comparison of reconstruction quality (PSNR) vs. the number of trainable parameters (M). Across all three images, our method consistently outperforms Instant-NGP (I-NGP) and MetricGrid, achieving a superior Pareto frontier and higher fidelity at every parameter scale.

Method	I-NGP [ 28 ]			NeuRBF [ 6 ]	MetricGrid [ 46 ]			Ours
Params (M)	8.01	32.01	412.8	115.4	8.02	32.02	412.8	8.02	28.24	114.6	418.5
PSNR $\uparrow$	21.51	27.3	33.05	31.56	27.03	29.70	37.06	27.53	31.33	37.07	43.37
SSIM $\uparrow$	0.579	0.896	0.959	0.960	0.817	0.957	0.994	0.897	0.984	0.998	0.999

Table 3: Numerical comparison on gigapixel girl image fitting. We report PSNR (dB), SSIM and the corresponding number of trainable parameters (in millions). Our method maintains competitive fidelity in both the low-parameter and high-parameter regimes.

Figure 5: Qualitative comparison on a gigapixel image. The leftmost presents the ground-truth image, while the three panels on the right visualize the per-pixel

\ell_{2}

error maps of I-NGP, MetricGrid, and the proposed method, respectively.

Method	I-NGP [ 28 ]			NeurRBF [ 6 ]	CINR [ 21 ]	MetricGrid [ 46 ]			Ours
Params (M)	95.45	214.02	402.6	161.48	157.24	95.46	199.25	390.01	18.24	93.53	233.57
PSNR $\uparrow$	40.97	41.68	42.06	40.30	40.69	41.06	42.19	43.03	41.24	42.24	44.02

Table 4: Numerical comparison on WSI image fitting. We report PSNR (dB) and the corresponding number of trainable parameters. Our method maintains competitive reconstruction fidelity in the low-parameter regime, while the high-capacity results are provided explicitly to facilitate direct numerical comparison in the large-model setting.

Figure 6: WSIs used for evaluation. Panel (a) four ultra-high-resolution WSIs from our collection; green boxes indicate regions shown at higher magnification, highlighting both global tissue architecture and cell-level morphology. Panel (b) patch-level visual comparison between a WSI patch from prior literature (left) and a patch from our raw scans (right): aggressive JPEG compression in the literature data introduces visible blocking artifacts, whereas our raw WSIs preserve fine structural detail. (Best viewed digitally with zoom). Panel (c) per-pixel

\ell_{2}

reconstruction error maps on a representative patch; CARA produces consistently lower error, indicating improved image fidelity.

	W.O. Collision Factor			W. Collision Factor
Params (K)	374	403	484	205	341	471
PSNR $\uparrow$	40.32	43.97	47.97	41.03	46.24	48.00
SSIM $\uparrow$	0.9674	0.9973	0.9979	0.9714	0.9906	0.9987

Table 5: Ablation of the collision factor

w^{\text{hash}}

on Kodak. Disabling collision modeling degrades PSNR/SSIM while typically requiring more parameters to reach comparable quality, highlighting the importance of explicitly accounting for hash collisions.

Method	I-NGP [ 28 ]		MetricGrid [ 46 ]		Ours+ $\ell_{2}$		Ours+var		Ours+entropy
Params (K)	206	300	207	335	214	334	211	331	205	332
PSNR $\uparrow$	37.06	43.88	39.73	44.51	38.52	43.60	38.74	44.94	41.03	46.63
SSIM $\uparrow$	0.9386	0.9964	0.9568	0.9978	0.9504	0.9913	0.9560	0.9893	0.9714	0.9982

Table 6: Effect of alternative information proxies for resolution scheduling on Kodak. We replace the entropy-based band information in Equation 7 with an

\ell_{2}

energy proxy (Ours +

\ell_{2}

); variance proxy (Ours + var) and compare against the entropy proxy (Ours + entropy); entropy consistently yields higher PSNR/SSIM.

Data	Kodak				Tokyo
Hash Model	Uniform		Empirical		Uniform		Empirical
Params	205K	341K	206K	344K	66.34M	123.4M	66.29	126.64 M
PSNR	41.03	46.24	41.07	46.03	35.01	37.22	35.04	37.17
SSIM	0.9714	0.9906	0.9713	0.9902	0.9145	0.9424	0.9163	0.9427

Table S1 : Comparison of the uniform-hash model in CARA and an empirical occupancy-based alternative on Kodak and Tokyo. The empirical variant does not provide a consistent improvement in PSNR or SSIM across parameter budgets. This indicates that the analytic uniform-hash assumption is sufficiently accurate for collision-aware resolution scheduling, while being simpler and more tractable.

Data	Kodak				Tokyo
	PSNR	SSIM	Time	Params (K)	PSNR	SSIM	Time	Params (M)
Instant-NGP [ 28 ]	38.70	0.9386	589s	207	36.26	0.9281	2230s	128.0
MetricGrids [ 8 ]	39.73	0.9568	1722s	207	35.19	0.9578	4180s	128.1
Ours	41.03	0.9714	592s	205	37.22	0.9424	2252s	123.4

Table S2 : Wall-clock training time, reconstruction quality, and parameter count of Instant-NGP, MetricGrids, and CARA on the Kodak dataset and the Tokyo gigapixel image. All methods are trained for the same number of epochs.

Method	I-NGP [ 28 ]			NeuRBF [ 6 ]	MetricGrid [ 46 ]			Ours
Params (M)	16.01	64.01	217.3	57.46	8.02	128.02	217.4	7.89	48.07	108.23	202.9
PSNR $\uparrow$	40.37	54.66	61.54	53.35	41.51	61.2	63.51	42.52	54.94	64.32	65.56
SSIM $\uparrow$	0.9584	0.9983	0.9996	0.9924	0.9585	0.9996	0.9998	0.9778	0.9873	0.9999	0.9999

Table S3 : Numerical comparison on gigapixel Pluto image fitting. We report PSNR (dB), SSIM and the corresponding number of trainable parameters (in millions). Our method maintains competitive fidelity in both the low and high-parameter regimes.

Figure S1 : Qualitative comparison on the Pluto gigapixel image. The left panel presents the ground-truth image, while the remaining panels show per-pixel

\ell_{2}

error maps for Instant-NGP, MetricGrid, and the proposed method, respectively. Brighter colors correspond to larger reconstruction error. Although MetricGrid improves over Instant-NGP on this example, our method yields the lowest residual error overall and achieves the highest PSNR (65.56 dB) while using fewer parameters, indicating a superior fidelity–parameter trade-off.

Method	I-NGP [ 28 ]			NeuRBF [ 6 ]	MetricGrid [ 46 ]			Ours
Params (M)	8.01	128.0	442.4	131.7	16.01	128.1	442.6	6.55	66.34	123.4	468.0
PSNR $\uparrow$	18.56	36.26	38.45	34.32	24.72	35.19	37.75	24.64	35.01	37.22	41.85
SSIM $\uparrow$	0.3212	0.9281	0.9362	0.8936	0.8173	0.9578	0.9423	0.8424	0.9145	0.9424	0.9916

Table S4 : Numerical comparison on gigapixel Tokyo image fitting. We report PSNR (dB), SSIM and the corresponding number of trainable parameters (in millions). Our method maintains competitive fidelity in both the low and high-parameter regimes.

Figure S2 : Qualitative comparison on the Tokyo gigapixel image. The left-up panel shows the ground-truth image, and the remaining panels visualize per-pixel

\ell_{2}

error maps for Instant-NGP, MetricGrid, and the proposed method, respectively. Brighter colors indicate larger reconstruction error. Notably, on this image, MetricGrid underperforms Instant-NGP despite using a comparable parameter budget, yielding both a lower PSNR (36.47 dB vs. 38.00 dB) and visibly larger high-error regions. In contrast, our method produces the lowest residual error and the highest reconstruction fidelity (39.24 dB), demonstrating the benefit of collision-aware, data-adaptive resolution allocation on challenging gigapixel scenes.

Figure S3 : Slide 1 and selected patch regions. Left: downsampled WSIs, where colored boxes indicate the spatial locations of the sampled patches. Right: the corresponding high-resolution selected patches extracted from the marked regions.

Figure S4 : Slide 2 and selected patch regions. Left: downsampled WSIs, where colored boxes indicate the spatial locations of the sampled patches. Right: the corresponding high-resolution selected patches extracted from the marked regions.

Figure S5 : Slide 3 and selected patch regions. Left: downsampled WSIs, where colored boxes indicate the spatial locations of the sampled patches. Right: the corresponding high-resolution selected patches extracted from the marked regions.

Figure S6 : Slide 4 and selected patch regions. Left: downsampled WSIs, where colored boxes indicate the spatial locations of the sampled patches. Right: the corresponding high-resolution selected patches extracted from the marked regions.

Data	Kodak			Pluto
Filter	Gaussian	Butterworth	Resize	Gaussian	Butterworth	Resize
Params	206.3 K	206 K	205 K	112.46 M	OOM	108.23 M
PSNR $\uparrow$	40.07	41.22	41.03	62.52	OOM	64.32
SSIM $\uparrow$	0.9576	0.9732	0.9714	0.9999	OOM	0.9999

Table S5 : Ablation of the low-pass filter used to estimate the band information density for CARA. We compare Gaussian filtering, Butterworth filtering, and anti-aliased resizing on Kodak and Pluto. Bold and underlined values denote the best and second-best results.

Tokyo Gigapixel Image
Shuffle Factor	PSNR $\uparrow$	SSIM $\uparrow$	Params (M)	PSNR $\uparrow$	SSIM $\uparrow$	Params (M)	PSNR $\uparrow$	SSIM $\uparrow$	Params (M)	PSNR $\uparrow$	SSIM $\uparrow$	Params (M)
$s=1$	18.69	0.3423	6.568	26.38	0.8134	25.39	35.52	0.9274	92.95	39.73	0.9612	247.6
$s=2$	24.64	0.8424	6.599	31.76	0.9091	23.93	34.66	0.9024	91.11	37.74	0.9434	238.8
$s=4$	18.21	0.4462	6.443	29.63	0.8612	22.42	32.52	0.8903	91.02	36.27	0.9225	236.4

Table S6 : Ablation of the pixel-shuffle folding factor

s

on the Tokyo gigapixel image across four comparable parameter budgets. We evaluate

s\in\{1,2,4\}

, where

s=1

denotes no pixel shuffle. Moderate shuffling (

s=2

) is most effective in the compact regimes, improving PSNR from

18.69

to

24.64

dB at

\sim

6.6M parameters and from

26.38

to

31.76

dB at

\sim

24M parameters. In contrast, at larger budgets (

\sim

91–93M and

\sim

239–248M parameters), the best performance is achieved without shuffling (

s=1

), while aggressive shuffling (

s=4

) is consistently inferior. These results show that pixel shuffle is a budget-dependent collision-mitigation strategy: it is beneficial when hash collisions are severe, but its advantage diminishes once the model has sufficient capacity.

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