Gestalt Laws Similarity Proximity Continuity Matrix

Encode independently witnessed Gestalt pair relations as symmetric bitmask matrix:1similarity,2proximity,4continuity. Multiple principles coexist; no automatic grouping or perception prediction.

Description

Several Gestalt grouping principles can be annotated for the same pair of elements.

Several Gestalt grouping principles can be annotated for the same pair of elements.^[1]

This tool encodes similarity, proximity and continuity links in a symmetric bitmask matrix.

When to use Gestalt Laws Similarity Proximity Continuity Matrix

Use this tool to encode similarity, proximity and continuity links in a symmetric bitmask matrix.

How to use Gestalt Laws Similarity Proximity Continuity Matrix and how it works

Establish the observations, units, reference context and assumptions described below.
Enter independentlyAnnotatedSimilarityLinks, independentlyAnnotatedProximityLinks, independentlyAnnotatedContinuityLinks, observedElementCount and run the tool.
Read result.pairPrincipleMaskMatrix using the meanings and sign conventions below.
Correct any rejected inputs and rerun; independently review the result under the stated scope.

Input field	Meaning	Value type	Requirement
independentlyAnnotatedSimilarityLinks	Independently annotated distinct zero-based element-index pairs for this principle; repeated undirected pairs within this list are rejected.	array of array of number	Required; branch conditions below
independentlyAnnotatedProximityLinks	Independently annotated distinct zero-based element-index pairs for this principle; repeated undirected pairs within this list are rejected.	array of array of number	Required; branch conditions below
independentlyAnnotatedContinuityLinks	Independently annotated distinct zero-based element-index pairs for this principle; repeated undirected pairs within this list are rejected.	array of array of number	Required; branch conditions below
observedElementCount	Integer number of indexed elements from 1 to 64.	number	Required; finite; branch conditions below

Supply an integer element count from 1 to 64 and three lists of zero-based index pairs for similarity, proximity and continuity. Empty link lists are allowed. Each pair must have two distinct in-range indices; reject duplicate undirected pairs within one principle, including reversed duplicates. Build a symmetric matrix with zero diagonal and OR masks 1, 2 and 4 for the corresponding links. One pair may carry multiple principles, giving combined masks through 7.

M[a][b]=M[b][a]=OR(similarity?1:0,proximity?2:0,continuity?4:0); M[a][a]=0

Use the stated ordering, units and branch conditions.

Output field	Meaning	Value type
result	Object containing the fields below.	object
result.pairPrincipleMaskMatrix	Symmetric matrix: similarity bit 1, proximity bit 2, continuity bit 4; zero diagonal.	array of array of number

json

{
  "input": {
    "independentlyAnnotatedSimilarityLinks": [
      [
        0,
        1
      ]
    ],
    "independentlyAnnotatedProximityLinks": [
      [
        1,
        2
      ]
    ],
    "independentlyAnnotatedContinuityLinks": [
      [
        0,
        2
      ]
    ],
    "observedElementCount": 3
  },
  "output": {
    "result": {
      "pairPrincipleMaskMatrix": [
        [
          0,
          1,
          4
        ],
        [
          1,
          0,
          2
        ],
        [
          4,
          2,
          0
        ]
      ]
    }
  }
}

Limitations and assumptions

The calculation depends on independently established observations, coefficients and the matching units. It does not collect data, choose a treatment or target, establish model applicability or provide a validated forecast. Interpret its result within the branch conditions and assumptions above.

Supply explicit values and dense aligned arrays. Unexpected fields, wrong types and nonfinite scalar values are rejected; fixed-token, alignment and other branch conditions are explained above. A successful false flag, empty match list or unknown-evidence list differs from an input error. Extremely large inputs or nonrepresentable results may fail.

Alternative or Complementary methods

Use Visual Rhythm Motif Repetition Interval Counter for a related operation: Visual repetition can be summarized through intervals between independently identified instances of one motif.

Use Rule of Thirds Composition Grid Checker for a related operation: A rule-of-thirds grid places lines at one third and two thirds of normalized image dimensions.

References

Gestalt Laws Similarity Proximity Continuity Matrix — tool.io

Similar or alternative tools

Visual Rhythm Motif Repetition Interval Counter
Visual repetition can be summarized through intervals between independently identified instances of one motif.
Rule of Thirds Composition Grid Checker
A rule-of-thirds grid places lines at one third and two thirds of normalized image dimensions.