EP04_07 — ⛰️ Weighted Dilation and Erosion (mm.dil1 / mm.ero1)

4.9.7.1 📋 Implementation Guidelines

1. Image dimensions: Read the integers \(L\) (rows) and \(C\) (columns) from \(f\).
2. Dimensions of \(b\): Read the integers \(L_B\) (rows) and \(C_B\) (columns) of the weighted structuring element.
3. Weights: Read the matrix \(b\) of integer weights (which may be negative, zero, or positive), row by row.
4. Data: Read the matrix \(f\) (the original image), row by row.
5. Neighborhood without padding: For each pixel \((y,x)\), iterate over all positions \((by,bx)\) of \(b\) (not only where it would equal \(1\) — here every weight participates), using the same offset as in previous EPs: \[ v_y = y + by + o_y,\quad v_x = x + bx + o_x,\quad o_y=-\tfrac{L_B}{2}+0{,}5,\quad o_x=-\tfrac{C_B}{2}+0{,}5 \] Discard every \((v_y,v_x)\) outside \([0,L)\times[0,C)\).
6. Weighted dilation: Compute \[ g_{dil}(y,x) = \max\Big(f(y,x),\ \max_{(v_y,v_x)\ \text{valid}} \big(f(v_y,v_x) + b(by,bx)\big)\Big) \]
7. Weighted erosion: Compute, using the same \(b\) and without reflection: \[ g_{ero}(y,x) = \min\Big(f(y,x),\ \min_{(v_y,v_x)\ \text{valid}} \big(f(v_y,v_x) - b(by,bx)\big)\Big) \]
8. Output: Display first the complete matrix \(g_{dil}\), and then the complete matrix \(g_{ero}\).

4.9.7.2 📌 Computational Constraints

• Neither reflects \(b\) — the weighted version does not use reflection, even in dilation (unlike mm.dil0).
• All weights participate: There is no “\(B=1\)” filter here; even weight \(0\) is included in the computation.
• No padding: neighbors outside the image are ignored, never virtually filled.
• Type: The output may contain negative values or values greater than \(255\) — there is no clipping in this EP.
• Hint: To remove overflow messages when exceeding uint8 limits, include at the beginning of the code:

import warnings
warnings.filterwarnings("ignore")

4.9.7.3 🧠 Theoretical Foundation

4.9.7.4 📦 Input and Output Specification (VPL)

Input:

• Line 1: Integer \(L\).
• Line 2: Integer \(C\).
• Line 3: Integer \(L_B\).
• Line 4: Integer \(C_B\).
• Next \(L_B\) lines: integer elements (may be negative) of the matrix \(b\).
• Next \(L\) lines: integer elements of the matrix \(f\).

Output:

• First, the matrix \(g_{dil}\) in \(L\) rows and \(C\) columns.
• Then, the matrix \(g_{ero}\) in \(L\) rows and \(C\) columns.

4.9.7.5 📌 Examples

%%writefile EP04_07.py
# Python code

Overwriting EP04_07.py

TestSuite("EP04_07.py").run()

✔️ EP04_07.cases already exists in casos/
📋 3 case(s) loaded from casos/EP04_07.cases

🔍 Testing Python: EP04_07.py
⚠️ EP04_07.py: Empty file (fewer than 3 lines). Tests skipped.