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

Mechanism

Quadrant decomposition is the spatial sub-region fingerprinting stage that follows global variance vector extraction. After the global nine-dimensional variance vector is computed for a content artifact, the same artifact is processed through a spatial decomposition pipeline that produces independent fingerprints for four non-overlapping quadrant regions. The purpose stated in the disclosure is concrete: to enable detection of partial similarity, regional mutation, and spatial composition matching that is not captured by the global nine-dimensional vector alone. The global vector answers whether two artifacts are structurally similar overall; the quadrant fingerprints answer where, spatially, they agree and where they diverge.

The decomposition is not a free-standing scheme. Each quadrant is run through the identical nine-dimensional extraction pipeline used for the global vector, so a quadrant fingerprint is a global-style fingerprint computed over one quarter of the canonical image. The four quadrant hashes are then combined with the global variance hash to form a single 320-bit unique identifier. Spatial localization and global identity are produced in one construction rather than as separate records.

Canonical Normalization

Before any quadrant can be extracted, the artifact is placed in a consistent coordinate space. The canonical normalization stage rescales the input artifact to a square canvas of 256 pixels by 256 pixels. It computes the ratio of the target dimension to the longest edge of the source artifact, applies uniform scaling along both dimensions to preserve aspect ratio, and centers the scaled image on a black background fill. This letterbox-style normalization ensures that all artifacts, regardless of original resolution or aspect ratio, occupy the same canonical coordinate space so that the four quadrant boundaries always partition comparable regions. Image smoothing is disabled during rescaling, which the disclosure notes is to prevent anti-aliasing from introducing artificial variance signals along rescaled edges.

Orientation Canonicalization

The orientation canonicalization module computes the dominant gradient orientation of the normalized artifact by extracting the peak bin of an eight-bin gradient histogram taken over the full canonical image. If the dominant orientation angle exceeds an absolute value of approximately 0.1 radians, corresponding to approximately 5.7 degrees, the artifact is rotated by that angle about the center of the canvas before quadrant extraction. This step presents artifacts with predominant orientation structure in a consistent spatial frame prior to spatial decomposition, which the disclosure states reduces inter-format and inter-resolution drift in the identifier attributable to minor rotational variations.

Quadrant Extraction and Per-Quadrant Vectors

Four spatial quadrant extraction modules extract non-overlapping rectangular sub-images from the canonical image: the top-left quadrant, the top-right quadrant, the bottom-left quadrant, and the bottom-right quadrant, each comprising one quarter of the canonical image area. Per-quadrant variance vector computation then applies the full nine-dimensional extraction pipeline described for the global vector to each quadrant sub-image, producing an independent X, Y, Z triplet for each spatial region. The X axis encodes cross-scale energy distribution, the Y axis cross-scale frequency compaction, and the Z axis structural phase persistence based on gradient orientation distribution, computed within the bounds of that quadrant alone.

Because each quadrant vector is computed only over the pixels inside its sub-image, a change confined to one spatial region affects that region's vector while leaving the others unchanged. This is the structural basis for the localized mutation detection the disclosure describes, and it follows directly from extracting each fingerprint from a disjoint sub-region of the canonical canvas.

Per-Quadrant Hashing

Per-quadrant hashing converts each quadrant's nine-dimensional vector into a 256-bit hexadecimal hash using a coarsened quantization scheme relative to the global hash: the X and Y axis components are quantized at a step of 1/32 and the Z axis components at a step of 1/8 prior to hashing. The disclosure explains the rationale for the coarser quantization: it absorbs JPEG compression noise and format conversion artifacts at the sub-image level, where localized compression introduces greater per-pixel variance than at the full-image level. The hash function applies multiple overlapping FNV (Fowler-Noll-Vo) variant hash functions at two quantization scales, 16 and 20, and XORs the resulting 128-bit outputs to produce the final 256-bit quadrant hash.

Rotation-Invariant Sorting and 320-Bit Construction

The rotation-invariant quadrant sorting module sorts the four quadrant hashes in lexicographic order of their hexadecimal string representations, then assigns the sorted hashes to canonical positions q0 through q3. Sorting makes the assignment of quadrant identifiers independent of the spatial orientation of the artifact, so that a rotated or mirrored version of an artifact produces the same set of sorted quadrant hashes even when the individual spatial positions of the quadrants differ.

The combined 320-bit unique identifier construction module applies a multi-segment FNV-64 hash combiner to the global 256-bit hash and the four sorted quadrant hashes, producing five 64-bit hash segments that are concatenated to form a 320-bit UID. The combiner applies five distinct initialization seeds to the same ordered concatenation of hash inputs, yielding five independent 64-bit outputs that together constitute an address space of 2 to the 320th power distinct UIDs. The disclosure states this address space is sufficient to ensure negligible collision probability across any foreseeable scale of digital content deployment. The first 16 hexadecimal characters, representing 64 bits, serve as a backward-compatible short-form identifier suitable for human-readable display, database indexing, and bandwidth-constrained transmission, while the full 320-bit representation is used for anchor node assignment, slope-band routing, and similarity comparison.

Localized Mutation Detection

The quadrant fingerprints become useful at comparison time. The comparison framework operates on UID records and produces per-axis cosine similarity scores for the X, Y, and Z axes, an aggregate directional cosine similarity, a Euclidean distance-based similarity score, and per-quadrant similarity scores together with hash match flags. The quadrant-level comparison supports localized mutation detection: a derivative artifact that modifies only one spatial region of a source exhibits quadrant similarity scores near 1.0 for the unchanged regions and reduced scores for the modified region, enabling spatially resolved attribution even when the global similarity score remains high. The disclosure frames this as the capability the global nine-dimensional vector cannot provide on its own, detecting not only that an artifact has changed but which region changed.

Application Across Modalities

Quadrant decomposition is defined over image artifacts in the canonical 256 by 256 pixel space, and the disclosure carries it into other modalities through that image pipeline rather than by redefining the partition. For video artifacts, UID derivation operates at two levels: at the frame level, each frame is treated as a raster image artifact and processed through the full image extraction pipeline, including canonical normalization, orientation canonicalization, global variance vector extraction, and quadrant decomposition; at the clip level, a temporal delta vector is derived from the cosine similarity between consecutive frame variance vectors. Audio artifacts are first reduced to a normalized mel-spectrogram, a two-dimensional scalar field, which is then processed through the same multi-axis variance extraction pipeline. In each case the quadrant construction described here is reused as defined rather than reinvented per modality.

Disclosure Scope

Quadrant decomposition and 320-bit UID construction, comprising canonical normalization to a 256 by 256 pixel square canvas, orientation canonicalization by dominant gradient orientation, extraction of four non-overlapping quadrant sub-images, per-quadrant computation of the nine-dimensional variance vector, per-quadrant hashing under the coarsened quantization scheme with FNV-variant functions at scales 16 and 20, rotation-invariant lexicographic sorting of the quadrant hashes into canonical positions q0 through q3, and combination of the global 256-bit hash with the four sorted quadrant hashes through a five-seed multi-segment FNV-64 combiner to form a 320-bit unique identifier, is disclosed in PCT International Application No. PCT/US26/28630, "Content Anchoring Through Structural Variance Analysis," at Section 3, with the corresponding comparison behavior at the localized-mutation-detection passage in Section 8 and a system claim reciting the same construction. This article describes that disclosed mechanism. The scope extends to the per-quadrant similarity comparison that produces quadrant similarity scores and hash match flags for spatially resolved attribution, and to the application of the construction to video frames and to scalar-field representations of audio through the same image extraction pipeline.