Binary Mask Explicit Stencil Gradient

Description

Calculate a signed morphological gradient as dilation minus erosion, preserving possible negative values.

A binary grid represents foreground as numeric one and background as zero. A stencil is a set of integer [rowOffset,columnOffset] positions relative to a cell. Connectivity describes allowed neighbor steps: four-neighbor connectivity uses orthogonal steps, while eight-neighbor connectivity also includes diagonals. Finite image borders and asymmetric stencils affect the result.

Calculate a signed morphological gradient as dilation minus erosion, preserving possible negative values.

When to use this tool

Use this difference grid to inspect where dilation and erosion disagree, retaining sign evidence.

How to use the tool and how it works

Enter mask, stencil using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.mask, using the stated boundary, ordering, sign and absence conventions.

Compute dilation and erosion independently from the original mask, then return dilation minus erosion cellwise.^[1]

Input field	Meaning and units	Accepted input
mask	Rectangular numeric 0/1 rows, up to 64×64; row is the first coordinate and column the second.	Dense numeric rows, each dimension at most 128; the stated shape rules also apply.
stencil	Nonempty list of distinct integer [rowOffset,columnOffset] pairs, each coordinate -16 through 16; at most 128 offsets.	Dense numeric rows, each dimension at most 128; the stated shape rules also apply.

Output field	Interpretation
result	Object containing the fields below.
result.mask	Result grid in original frame dimensions, with numeric cell meanings and any signed subtraction convention described above.

json

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

Limitations and assumptions

The result is a signed numeric difference, not necessarily binary. With a stencil that omits the origin, erosion can be one where dilation is zero, producing -1.
Masks are rectangular dense arrays of numeric 0/1 cells, with at most 64 rows and 64 columns. Empty frames are allowed where no in-bounds seed is required. Stencils are nonempty lists of distinct integer [rowOffset,columnOffset] pairs, each coordinate between -16 and 16. Outside-frame samples are zero at every stage.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Numeric outputs must remain finite and within safe-integer magnitude. Original record indexes and cell coordinates are zero-based; stated half-open ranges exclude their end.

Alternative or Complementary methods

Choose a component operation for connected regions and an explicit stencil for local shape tests. Fix connectivity and border policy before comparing masks; convert cell counts to physical area separately when pixel spacing is known.

References

Tool behavior and example: Binary Mask Explicit Stencil Gradient — tool.io

Similar or alternative tools

Binary Mask Explicit Stencil Dilation
Dilate a binary mask using reflected-offset source positions from the supplied stencil.
Binary Mask Explicit Stencil Erosion
Erode a binary mask using every positive-offset source position in the supplied stencil.