Grid Mask Chebyshev Dilation

Apply chebyshev binary morphology in the original grid, radius 0–8, treating outside cells as zero; no automatic resizing or physical-distance model.

Description

Apply chebyshev binary morphology in the original grid, radius 0–8, treating outside cells as zero; no automatic resizing or physical-distance model.

Chebyshev dilation expands set cells through a square-radius neighborhood, including diagonal offsets.

When to use this tool

Apply chebyshev binary morphology in the original grid, radius 0–8, treating outside cells as zero; no automatic resizing or physical-distance model.

Prepare the supplied mask, radius fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter mask, radius. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.mask. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

For radius 0 to 8, set each output cell if any one occurs within that row/column offset square, reading outside positions as unset.^[1]

Input field	Meaning and representation	Accepted input
mask	mask.	Numeric rows; at most 128 rows and 128 values per row
radius	radius.	Integer from 0 to 8 inclusive

Output field	Interpretation
result	Object containing the named outputs below.
result.mask	The mask list in the ordering and representation described above.

json

{
  "input": {
    "mask": [
      [
        0,
        0,
        0
      ],
      [
        0,
        1,
        0
      ],
      [
        0,
        0,
        0
      ]
    ],
    "radius": 1
  },
  "output": {
    "result": {
      "mask": [
        [
          1,
          1,
          1
        ],
        [
          1,
          1,
          1
        ],
        [
          1,
          1,
          1
        ]
      ]
    }
  }
}

Limitations and assumptions

No new outer rows or columns are added. Radius zero returns the original membership pattern.
Coordinate pairs use [row,column] where stated. Masks are nonempty rectangular zero/one matrices of at most 128 rows, 128 columns and 16,384 cells; outside-mask values are unset for the neighborhood operations.
Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
String lists have at most 128 entries of at most 128 code units; matrices have at most 128 rows and columns. Larger numeric lists and parsed JSON have separate bounded budgets. Nonfinite results and excessively large serialized outputs are rejected.
Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.

Alternative or Complementary methods

Keep row/column coordinates distinct from x/y pairs and byte offsets. Select the neighborhood metric, outside-mask rule and storage-order convention explicitly; these operations do not infer an image format.

References

Tool behavior and example: Grid Mask Chebyshev Dilation — tool.io

Similar or alternative tools

Grid Mask Manhattan Dilation
Apply manhattan binary morphology in the original grid, radius 0–8, treating outside cells as zero; no automatic resizing or physical-distance model.
Grid Mask Boolean Combination
Combine identically shaped binary masks by explicit AND, OR, XOR or left difference; no resampling or alignment inference.