Quadrant Decomposition: Spatial Sub-Region Fingerprinting for Partial Similarity Detection

Mechanism

The decomposition partitions the spatial extent of the content into four equal, non-overlapping regions arranged in a two-by-two grid. For raster imagery the regions are pixel rectangles; for video the regions are spatiotemporal volumes whose temporal extent is the entire clip; for documents the regions are page sub-rectangles defined relative to the canonical layout; for audio the regions are time-frequency tiles defined relative to a fixed spectrogram framing. The partition is parameter-free in the sense that the geometry is fully determined by the canonical extent of the content, eliminating any ambiguity about which bytes contribute to which region.

Each region is fed independently to the same deterministic variance extractor used for the global anchor. The extractor produces a fixed-dimension vector for each region, yielding four regional vectors of identical dimension. A global vector is also produced over the unrestricted content. The composite anchor then carries five vectors, each labeled by its region identifier, along with the metadata, lineage reference, and signature that the global anchor would carry on its own. The cost of the additional fingerprints is bounded: each regional extraction is performed on roughly one quarter of the data, so the aggregate extraction cost is approximately twice the cost of the global anchor alone, and the storage cost grows linearly with the number of vectors.

Verification proceeds region by region. A verifier presented with candidate content and a composite anchor performs the same partition on the candidate, recomputes the four regional vectors and the global vector, and compares each recomputed vector against the corresponding vector in the anchor. The outcome is no longer a single bit but a five-component vector of match/mismatch results. A modification confined to the upper-left quadrant produces a profile in which the upper-left regional vector and the global vector both mismatch while the other three regional vectors match; this profile constitutes a localization claim that the verifier can act on directly.

The localization property is structural rather than statistical. Because each regional vector is a deterministic function of the bytes inside its region alone, a region whose bytes are unchanged necessarily yields an unchanged regional vector, and a region whose bytes are changed necessarily yields a changed vector subject to the extractor's sensitivity floor. The verifier therefore receives a precise account of which regions have been disturbed, not a probabilistic estimate. This precision is what distinguishes differential anchoring from monolithic fingerprinting, which can detect that something has changed but cannot say what.

Partial similarity detection follows from the same machinery. Two pieces of content that share three quadrants and differ in the fourth produce composite anchors with three matching regional vectors, and a verifier comparing the two anchors directly, without access to either content, can establish the partial overlap. This makes the construction useful for tasks such as identifying derivative works, detecting cropped reuse, and tracing fragments through a redistribution graph, none of which require comparing the original content bytes.

Operating Parameters

The number of regions is fixed at four for the canonical embodiment because four-way decomposition balances localization granularity against anchor size and is uniformly defined for the content classes the architecture targets. Deployments requiring finer localization may apply the decomposition recursively to obtain sixteen or sixty-four regions, accepting the corresponding linear growth in anchor size and extraction cost. Recursive decomposition is itself parameter-free given a fixed depth.

Region boundaries are defined relative to the canonical extent of the content, which for imagery is the declared pixel dimensions, for video is the declared frame dimensions and clip duration, for documents is the canonical page rectangle, and for audio is the declared sample count and channel layout. Content that has been padded, cropped, or otherwise resized is realigned to its canonical extent before decomposition; the realignment rule is part of the deployment specification and is the same on the production side and the verification side.

Each regional vector inherits the dimension, feature basis, sensitivity floor, and quantization rule of the global vector. Using a uniform extractor across regions ensures that the match/mismatch decision in each region is governed by the same threshold, so that a verifier can interpret the five-component result without per-region calibration. Deployments that require asymmetric sensitivity, for example to be more tolerant of changes in peripheral regions than in central ones, may attach per-region thresholds to the anchor; the thresholds are themselves part of the signed record.

The composite anchor's signature covers all five vectors, the region geometry parameters, and the metadata in a single signing operation, so that an adversary cannot substitute a regional vector without breaking the signature over the whole anchor. Lineage chaining operates over the composite anchor as a unit, with the prior-anchor reference pointing at the composite predecessor rather than at any individual regional vector.

Anchor size grows from a single vector plus metadata to five vectors plus metadata, a roughly five-fold increase that remains bounded in absolute terms because each vector is small. For typical configurations the composite anchor remains well under a kilobyte, preserving the bandwidth-efficiency property that the broader anchoring architecture provides.

Alternative Embodiments

In one embodiment, the four-way decomposition is applied recursively to fixed depth, producing a hierarchical anchor in which each level localizes more precisely. A verifier may evaluate only the top level for fast acceptance and descend to deeper levels only when the top level reports a mismatch, providing efficient triage at scale. In another, the decomposition uses content-aware region boundaries derived from a deterministic segmentation of the content, allowing regions to align with semantic structures such as faces, paragraphs, or speakers rather than with a fixed grid; the segmentation rule is itself part of the deployment specification so that producer and verifier compute identical regions.

For temporal media, an embodiment defines regions as time slices in addition to or instead of spatial quadrants, allowing localization in time as well as space. For multi-channel audio, regions may be defined by channel and frequency band. For documents, regions may be defined by structural element rather than geometric rectangle. In each case, the structural property that each regional vector depends only on the bytes inside its region is preserved, so that the localization guarantee carries over.

A verification embodiment displays the five-component result as a heat map overlaid on the candidate content, giving operators an immediate visual indication of where alterations have occurred. An archival embodiment indexes content by regional vector so that searches over a corpus can locate items sharing a specific quadrant with a query, supporting forensic investigation of fragment reuse.

Composition with Other Architectural Primitives

Quadrant decomposition composes naturally with client-side execution: the regional and global extractions are performed in the same on-device pass, so the privacy and bandwidth properties of the broader anchoring architecture extend to the regional fingerprints without modification. It composes with the lineage substrate by treating the composite anchor as the unit of chaining, so that the per-region history of a piece of content can be reconstructed from the lineage without holding the content. It composes with policy enforcement by allowing acceptance rules at distribution points to be expressed at the region level: a platform may accept content whose central region matches an authorized anchor while remaining indifferent to peripheral changes, or vice versa, with the rule expressed once and enforced uniformly.

The construction also composes with selective disclosure: a producer can disclose a single region of a piece of content to a verifier and prove that the disclosed region matches the corresponding regional vector in the anchor, without disclosing the other three regions. This region-level zero-knowledge property is a direct consequence of the per-region fingerprint binding and requires no additional cryptographic protocol.

Prior-Art Distinction

Conventional perceptual hashing produces a single fingerprint for an entire piece of content and therefore cannot localize alterations; a verifier learns that the content has changed but not where. Block-based hashing schemes used in storage systems partition content into fixed-size blocks for deduplication or integrity checking, but they hash bytes directly and so are not robust to representational nuisances; any transcoding invalidates every block. Tile-based image hashing has been explored for near-duplicate detection but is typically used as an internal feature for similarity search rather than as a signed, lineage-bound provenance record. Watermarking schemes that embed region-specific markers alter the content and remain vulnerable to adversarial removal.

The construction described here differs by combining structural variance extraction, which is robust to representational nuisances, with a parameter-free spatial decomposition, a uniform sensitivity threshold across regions, and a single signature binding the regional vectors together with the global vector and the lineage reference. The result is a provenance record that simultaneously supports global authenticity verification, region-level tamper localization, and partial-similarity detection over anchors alone, without requiring access to the underlying content at verification time.

Disclosure Scope

The mechanism is disclosed in support of US 63/808,372, "Content Anchoring Through Structural Variance Analysis." The disclosure encompasses the four-way spatial decomposition, the per-region application of the deterministic variance extractor, the composite anchor format binding regional and global vectors under a single signature, the recursive and content-aware decomposition variants, and the verification protocol that produces a per-region match/mismatch result. Embodiments that vary the region count, the boundary rule, or the host modality remain within scope so long as the regional fingerprints are independent functions of the bytes inside their respective regions, the regional and global fingerprints are bound under a single signature, and verification yields a per-region localization result.

Licensing inquiries and implementation guidance are available through the publication channels referenced above. The disclosure is intended to support both defensive publication and active prosecution, and is offered without warranty as to fitness for any particular deployment.

The disclosure further contemplates the operational discipline by which the regional decomposition specification is communicated between producer and verifier so that both parties partition identical bytes into identical regions. The specification includes a canonical extent declaration, a realignment rule for content that arrives in a non-canonical container, a tie-breaking rule for region boundaries that fall on fractional pixel or sample positions, and a definition of how padded or truncated content is handled before decomposition. Each of these elements is necessary because the localization guarantee depends on identical region byte sets on both sides of the verification, and any divergence in the partition would manifest as spurious mismatches that are indistinguishable from genuine alterations. The specification, together with conformance test vectors exercising boundary conditions, is part of the deployment package and is itself anchored under the same lineage discipline that governs the content anchors, so that producer and verifier can prove they are operating against the same partition rules even across long retention horizons during which implementations may evolve.