Convolution.cs

using System;
using System.Drawing;

namespace Convolution
{
    public class Convolution
    {
        public Image DoMagic(Bitmap input, ConvolutionKernel kernel)
        {
            var output = new Bitmap(input.Width, input.Height);
            var s = kernel.Size / 2;

            for (var x = s; x < input.Width - s; x++)
            {
                for (var y = s; y < input.Height - s; y++)
                {
                    int r = 0, b = 0, g = 0;

                    for (var i = 0; i < kernel.Size; i++)
                    {
                        for (var j = 0; j < kernel.Size; j++)
                        {
                            var temp = input.GetPixel(x + i - s, y + j - s);

                            r += kernel.Matrix[i, j] * temp.R;
                            g += kernel.Matrix[i, j] * temp.G;
                            b += kernel.Matrix[i, j] * temp.B;
                        }
                    }

                    r = Math.Min(Math.Max((r / kernel.Factor) + kernel.Offset, 0), 255);
                    g = Math.Min(Math.Max((g / kernel.Factor) + kernel.Offset, 0), 255);
                    b = Math.Min(Math.Max((b / kernel.Factor) + kernel.Offset, 0), 255);

                    output.SetPixel(x, y, Color.FromArgb(r, g, b));
                }
            }

            return output;
        }
    }
}

ConvolutionKernel.cs

namespace Convolution
{
    public class ConvolutionKernel
    {
        public int Factor { get; set; }
        public int Offset { get; set; }

        private int[,] _matrix =
            {
                {-2, -2, -2, -2, -2},
                {-1, -1, -1, -1, -1},
                {0, 0, 0, 0, 0},
                {1, 1, 1, 1, 1},
                {2, 2, 2, 2, 2}
            };

        public int[,] Matrix
        {
            get
            {
                return _matrix;
            }
            set
            {
                _matrix = value;
                Factor = 0;

                for (var i = 0; i < Size; i++)
                {
                    for (var j = 0; j < Size; j++)
                    {
                        Factor += _matrix[i, j];
                    }
                }

                if (Factor == 0)
                {
                    Factor = 1;
                }
            }
        }

        private int _size = 5;

        public int Size
        {
            get
            {
                return _size;
            }
            set
            {
                if (value != 1 && value != 3 && value != 5 && value != 7)
                {
                    _size = 5;
                }
                else
                {
                    _size = value;
                }
            }
        }

        public ConvolutionKernel()
        {
            Offset = 0;
            Factor = 1;
        }
    }
}

MainForm.cs

using System;
using System.Drawing;
using System.Windows.Forms;

namespace Convolution
{
    public partial class MainForm : Form
    {
        public MainForm()
        {
            InitializeComponent();
        }

        private void BtnSmallClick(object sender, EventArgs e)
        {
            var convolution = new Convolution();
            var source = new Bitmap(pbSource.Image);
            var kernel = new ConvolutionKernel();
            int[,] matrix = {{-1, -1, -1}, {0, 0, 0}, {1, 1, 1}};

            kernel.Size = 3;
            kernel.Matrix = matrix;

            var image = convolution.DoMagic(source, kernel);

            pbSmall.Image = image;
            Refresh();
        }

        private void BtnBigClick(object sender, EventArgs e)
        {
            var convolution = new Convolution();
            var source = new Bitmap(pbSource.Image);
            var kernel = new ConvolutionKernel();

            var image = convolution.DoMagic(source, kernel);

            pbBig.Image = image;
            Refresh();
        }
    }
}

MainForm.Designer.cs

namespace Convolution
{
    partial class MainForm
    {
        /// <summary>
        /// Required designer variable.
        /// </summary>
        private System.ComponentModel.IContainer components = null;

        /// <summary>
        /// Clean up any resources being used.
        /// </summary>
        /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param>
        protected override void Dispose(bool disposing)
        {
            if (disposing && (components != null))
            {
                components.Dispose();
            }
            base.Dispose(disposing);
        }

        #region Windows Form Designer generated code

        /// <summary>
        /// Required method for Designer support - do not modify
        /// the contents of this method with the code editor.
        /// </summary>
        private void InitializeComponent()
        {
            this.pbSource = new System.Windows.Forms.PictureBox();
            this.pbSmall = new System.Windows.Forms.PictureBox();
            this.btnSmall = new System.Windows.Forms.Button();
            this.pbBig = new System.Windows.Forms.PictureBox();
            this.btnBig = new System.Windows.Forms.Button();
            ((System.ComponentModel.ISupportInitialize)(this.pbSource)).BeginInit();
            ((System.ComponentModel.ISupportInitialize)(this.pbSmall)).BeginInit();
            ((System.ComponentModel.ISupportInitialize)(this.pbBig)).BeginInit();
            this.SuspendLayout();
            // 
            // pbSource
            // 
            this.pbSource.Image = global::Convolution.Properties.Resources.Fluttershy;
            this.pbSource.Location = new System.Drawing.Point(12, 12);
            this.pbSource.Name = "pbSource";
            this.pbSource.Size = new System.Drawing.Size(300, 340);
            this.pbSource.TabIndex = 0;
            this.pbSource.TabStop = false;
            // 
            // pbSmall
            // 
            this.pbSmall.Location = new System.Drawing.Point(318, 12);
            this.pbSmall.Name = "pbSmall";
            this.pbSmall.Size = new System.Drawing.Size(300, 340);
            this.pbSmall.TabIndex = 1;
            this.pbSmall.TabStop = false;
            // 
            // btnSmall
            // 
            this.btnSmall.Location = new System.Drawing.Point(318, 12);
            this.btnSmall.Name = "btnSmall";
            this.btnSmall.Size = new System.Drawing.Size(75, 23);
            this.btnSmall.TabIndex = 2;
            this.btnSmall.Text = "3*3";
            this.btnSmall.UseVisualStyleBackColor = true;
            this.btnSmall.Click += new System.EventHandler(this.BtnSmallClick);
            // 
            // pbBig
            // 
            this.pbBig.Location = new System.Drawing.Point(624, 12);
            this.pbBig.Name = "pbBig";
            this.pbBig.Size = new System.Drawing.Size(300, 340);
            this.pbBig.TabIndex = 3;
            this.pbBig.TabStop = false;
            // 
            // btnBig
            // 
            this.btnBig.Location = new System.Drawing.Point(624, 12);
            this.btnBig.Name = "btnBig";
            this.btnBig.Size = new System.Drawing.Size(75, 23);
            this.btnBig.TabIndex = 4;
            this.btnBig.Text = "5*5";
            this.btnBig.UseVisualStyleBackColor = true;
            this.btnBig.Click += new System.EventHandler(this.BtnBigClick);
            // 
            // MainForm
            // 
            this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
            this.ClientSize = new System.Drawing.Size(936, 364);
            this.Controls.Add(this.btnBig);
            this.Controls.Add(this.pbBig);
            this.Controls.Add(this.btnSmall);
            this.Controls.Add(this.pbSmall);
            this.Controls.Add(this.pbSource);
            this.Name = "MainForm";
            this.Text = "MainForm";
            ((System.ComponentModel.ISupportInitialize)(this.pbSource)).EndInit();
            ((System.ComponentModel.ISupportInitialize)(this.pbSmall)).EndInit();
            ((System.ComponentModel.ISupportInitialize)(this.pbBig)).EndInit();
            this.ResumeLayout(false);

        }

        #endregion

        private System.Windows.Forms.PictureBox pbSource;
        private System.Windows.Forms.PictureBox pbSmall;
        private System.Windows.Forms.Button btnSmall;
        private System.Windows.Forms.PictureBox pbBig;
        private System.Windows.Forms.Button btnBig;
    }
}

Program.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows.Forms;

namespace Convolution
{
    static class Program
    {
        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main()
        {
            Application.EnableVisualStyles();
            Application.SetCompatibleTextRenderingDefault(false);
            Application.Run(new MainForm());
        }
    }
}

Thanks for this, it is quite the help.