Grid Mask Bounding Rectangle

Find the smallest half-open row/column bounding rectangle of set binary mask cells; an all-zero mask has no rectangle.

Description

Find the smallest half-open row/column bounding rectangle of set binary mask cells; an all-zero mask has no rectangle.

A mask bounding rectangle encloses all set cells, while an all-zero mask has no occupied bound.

When to use this tool

Find the smallest half-open row/column bounding rectangle of set binary mask cells; an all-zero mask has no rectangle.

Prepare the supplied mask 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. 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.empty, result.bounds. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Find every one position. If any exist return minimum top/left and maximum row/column plus one as exclusive bottom/right; otherwise empty is true and bounds null.^[1]

Input field	Meaning and representation	Accepted input
mask	mask.	Numeric rows; at most 128 rows and 128 values per row

Output field	Interpretation
result	Object containing the named outputs below.
result.empty	Flag for empty under the exact condition described above.
result.bounds	The bounds value under the stated formula or text convention.

json

{
  "input": {
    "mask": [
      [
        0,
        1,
        0
      ],
      [
        0,
        0,
        1
      ]
    ]
  },
  "output": {
    "result": {
      "empty": false,
      "bounds": {
        "top": 0,
        "left": 1,
        "bottomExclusive": 2,
        "rightExclusive": 3
      }
    }
  }
}

Limitations and assumptions

The binary mask itself must be nonempty. The box can contain unset cells and does not identify separate components.
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 Bounding Rectangle — tool.io

Similar or alternative tools

Grid Mask Boolean Combination
Combine identically shaped binary masks by explicit AND, OR, XOR or left difference; no resampling or alignment inference.
Grid Mask Border Cells
List set binary mask cells adjacent to a four-neighbor unset/outside position in stable row-major order.