SCSSIM: Scene Composition Similarity Metric

• SCSSIM is an analytical, training-free metric that quantifies scene composition structure by evaluating geometric relationships among objects in an image.
• The metric employs a hierarchical cuboidal partitioning (CuPID) approach to recursively partition images and compute normalized cumulative-gain curves for robust structure comparison.
• SCSSIM is resilient to non-compositional distortions like noise and blur while sharply detecting compositional changes, making it ideal for assessing generative AI outputs.

The SCS Similarity Index Measure (SCSSIM) is an analytical, training-free metric designed to quantify the preservation of Scene Composition Structure (SCS) in images, particularly in the context of generative AI outputs and image quality assessment. SCSSIM addresses critical shortcomings of both pixel-level and perceptual metrics by explicitly capturing and comparing the geometric relationships—such as relative positions, orientations, and sizes—among objects and partitions in a scene. The measure exploits a hierarchical cuboidal partitioning (CuPID) strategy to robustly extract and compare the underlying composition structure, enabling rigorous, monotonic assessment of compositional changes while maintaining strong invariance to non-compositional distortions such as noise or blur (Haque et al., 7 Aug 2025).

1. Scene Composition Structure (SCS) and Metric Limitations

SCS refers to the arrangement of an image’s geometric and structural elements, defined by the positions, sizes, orientations of dominant objects, division lines (e.g., horizons), and compositional partitions. Traditional composition concepts, such as the "Rule of Thirds," offer a coarse manual grid, but SCS demands an algorithmic extraction of the most influential horizontal and vertical splits which govern scene layout. Existing similarity metrics—PSNR, SSIM, MS-SSIM—are highly sensitive to low-level perturbations and fail to capture SCS, while learned perceptual metrics (LPIPS, CLIP-Score, FID) remain largely invariant under major scene rearrangements, including rotation or cropping. As a result, none of these fulfill the dual desiderata for SCS similarity: (1) invariance under non-compositional distortions; (2) strict monotonicity of similarity in response to true composition alterations (Haque et al., 7 Aug 2025).

2. Formal Construction and Derivation of SCSSIM

SCSSIM is constructed atop the CuPID (Cuboidal Partitioning of Image Data) procedure, which recursively partitions an image using axis-aligned (horizontal or vertical) cuts that maximize the reduction in sum-of-squared-errors (SSE) of pixel features (typically in RGB space). By greedily selecting splits which induce the largest gain, CuPID constructs a binary partition tree representing the dominant structural axes of the image. Each cut contributes a gain $g_j$; the sequence $\{g_1, g_2, \ldots, g_{\tilde N}\}$ (with $\tilde N$ typically 64) reflects the hierarchy and strength of compositional boundaries.

For each image, a normalized cumulative-gain curve $c = (c_1, ..., c_{\tilde N})$ is constructed:

$c_i = \frac{1}{e} \sum_{j=1}^i g_j$

where $e$ is the overall SSE. The similarity between two images is assessed by applying the sequence of cuts from one onto the other, comparing cumulative-gain curves in log-space to account for proportionality:

$k_i = \log \left( \frac{c_i}{c_{0,i}} \right)$

The average log-deviation $\bar k$ over all cuts is then mapped to a similarity value via a Gaussian-like decay:

$M(I, I_0) = \exp(-\lambda \cdot \bar k^2)$

with $\lambda$ as a sensitivity parameter. To ensure symmetry, the final SCSSIM is defined as the mean of $\{g_1, g_2, \ldots, g_{\tilde N}\}$0 and $\{g_1, g_2, \ldots, g_{\tilde N}\}$1. This strictly bounds SCSSIM within $\{g_1, g_2, \ldots, g_{\tilde N}\}$2, with 1 iff both images have identical SCS (Haque et al., 7 Aug 2025).

3. Algorithmic Steps and Pseudocode

The computation of SCSSIM proceeds through the following algorithmic stages:

1. CuPID Tree Construction: For each image, recursively partition via horizontal or vertical cuts that yield the maximum SSE gain, forming two sets of cut sequences $\{g_1, g_2, \ldots, g_{\tilde N}\}$3 and $\{g_1, g_2, \ldots, g_{\tilde N}\}$4 for the respective images.
2. Reference Curves Generation: For each image, compute its normalized cumulative-gain curve using its own partition tree.
3. Cross-application of Cuts: Apply each image’s partition sequence to the other image to compute cross-curves.
4. Directional Similarity Calculation: For each direction, calculate $\{g_1, g_2, \ldots, g_{\tilde N}\}$5 and $\{g_1, g_2, \ldots, g_{\tilde N}\}$6, then map to $\{g_1, g_2, \ldots, g_{\tilde N}\}$7 as above.
5. Symmetrization: Return the mean of both directional $\{g_1, g_2, \ldots, g_{\tilde N}\}$8 values.

The following table summarizes these computational steps for clarity:

Stage	Operation	Complexity
CuPID Partitioning	Build tree of $\{g_1, g_2, \ldots, g_{\tilde N}\}$9 cuts	$\tilde N$0
Cumulative-Gain Curve	Compute $\tilde N$1 for each partition	$\tilde N$2
Cross-Application	Apply $\tilde N$3 cuts to $\tilde N$4, $\tilde N$5 to $\tilde N$6	$\tilde N$7
Similarity Mapping	Compute $\tilde N$8, $\tilde N$9, $c = (c_1, ..., c_{\tilde N})$0	$c = (c_1, ..., c_{\tilde N})$1

Empirical timing indicates $c = (c_1, ..., c_{\tilde N})$2 s per $c = (c_1, ..., c_{\tilde N})$3 image pair for $c = (c_1, ..., c_{\tilde N})$4 on standard CPUs (Haque et al., 7 Aug 2025).

4. Mathematical Properties and Behavior

SCSSIM satisfies several critical mathematical and empirical properties:

• Boundedness and Identity: SCSSIM $c = (c_1, ..., c_{\tilde N})$5, with SCSSIM$c = (c_1, ..., c_{\tilde N})$6 by construction.
• Symmetry: Definitionally symmetric due to bidirectional averaging.
• Invariance: Strong invariance to non-compositional distortions; e.g., under significant Gaussian or salt-and-pepper noise or blur, SCSSIM remains $c = (c_1, ..., c_{\tilde N})$7 so long as compositional structure is preserved.
• Monotonicity: Under geometric modifications altering SCS (rotation, cropping, zooming, panning), similarity decays smoothly and strictly—as measured by increasing $c = (c_1, ..., c_{\tilde N})$8—unlike competing metrics such as SSIM, LPIPS, or CLIP.
• Discriminativity: SCSSIM demonstrates robust grouping of generative AI outputs by underlying SCS, showing intra-group similarity $c = (c_1, ..., c_{\tilde N})$9 and inter-group similarity $c_i = \frac{1}{e} \sum_{j=1}^i g_j$0 in experiments (Haque et al., 7 Aug 2025).

5. Experimental Evaluation

Experiments establish the practical effectiveness of SCSSIM in scenarios where other measures fail to capture structural fidelity. The SCSSIM metric was evaluated using the Kodak dataset with five test conditions—noisy, blurry, rotated, structurally similar, and structurally different images—alongside SSIM, MS-SSIM, LPIPS, and CLIP. Key results include:

Metric	Noisy	Blurry	Rotated	Similar Struct.	Diff. Struct.
SSIM	0.09	0.67	0.31	0.17	0.15
MS-SSIM	0.45	0.89	0.27	0.15	0.11
LPIPS	0.25	0.48	0.29	0.24	0.22
CLIP	0.81	0.94	0.93	0.70	0.59
SCSSIM	0.99	0.99	0.09	0.32	0.10

These results underscore that SCSSIM remains maximally high under non-compositional perturbations (noise, blur), but sharply decreases when true SCS is altered. Figure 1 in the referenced work demonstrates that only SCSSIM maintains close to $c_i = \frac{1}{e} \sum_{j=1}^i g_j$1 under increasing noise and blur, and only it exhibits a smooth, near-linear collapse under compositional changes (Haque et al., 7 Aug 2025).

6. Limitations and Practical Considerations

While SCSSIM demonstrates robust behavior for scene composition analysis, several limitations are noted:

• Fixed Cut Orientation: Only horizontal and vertical (axis-aligned) cuts are considered, so diagonal or non-rectilinear structures may not be optimally represented.
• Color-Space Dependence: All statistics rely on RGB features; extension to depth, semantics, or non-RGB modalities would require modifying the feature representation $c_i = \frac{1}{e} \sum_{j=1}^i g_j$2.
• Sensitivity at Extreme Distortions: Extreme texture-destroying effects (e.g., $c_i = \frac{1}{e} \sum_{j=1}^i g_j$3 salt-and-pepper noise) can degrade SCSSIM, not due to composition loss but due to the destruction of the SSE structure.
• Scale and Registration: Images must be geometrically registered. Misalignment or scaling discrepancies will affect the perceived SCS change, leading to decreased similarity—even if high-level structure is preserved (Haque et al., 7 Aug 2025).

7. Applications and Impact

SCSSIM has particular utility for evaluating generative model outputs where structural fidelity, rather than only perceptual similarity, is essential. It is instrumental for monitoring, benchmarking, and guiding the production of images where scene geometry and relational layout must remain consistent—especially in automated content generation, computer vision, and computational photography. The metric’s analytical, non-learned construction avoids training-phase biases and generalization errors encountered in deep learned metrics, supporting its adoption in scenarios requiring robust and interpretable SCS evaluation (Haque et al., 7 Aug 2025).