OpenCV_Homography.ipynb

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  "metadata": {
    "colab": {
      "name": "OpenCV_Homography.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
    {
      "metadata": {
        "id": "0ddKnhAv9q-H",
        "colab_type": "code",
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      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import cv2 as cv\n",
        "from matplotlib import pyplot as plt\n",
        "from google.colab.patches import cv2_imshow\n",
        "from google.colab import files\n",
        "from IPython.display import Image\n",
        "\n",
        "uploaded = files.upload()\n",
        "#img = cv.imread('man-of-steel.jpg')\n",
        "img = cv.imread('man-of-steel_small.jpg')\n",
        "img_rgb = cv.cvtColor(img, cv.COLOR_BGR2RGB)\n",
        "\n",
        "uploaded = files.upload()\n",
        "img_des = cv.imread('horrorposter-preview_distorted.jpg')\n",
        "img_des_rgb = cv.cvtColor(img_des, cv.COLOR_BGR2RGB)\n",
        "# the shape of this image\n",
        "print(img_rgb.shape)\n",
        "plt.imshow(img_rgb)\n",
        "plt.show()\n",
        "\n",
        "plt.imshow(img_des_rgb)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "zU8sDqiB92dn",
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      "cell_type": "code",
      "source": [
        "# A in AX=0\n",
        "MatrixA = np.zeros((8,9))\n",
        "\n",
        "# The Homography transformation matrix\n",
        "HomoMat = np.zeros((3,3))\n",
        "\n",
        "\n",
        "'''\n",
        "## image 1: The 4 corners of the input image: bigger input image: man-of-steel.jpg\n",
        "## point 1\n",
        "# top left\n",
        "img1_pt1 = np.array([[0],[0]])\n",
        "# top right\n",
        "img1_pt2 = np.array([[812],[0]])\n",
        "# bottom left\n",
        "img1_pt3 = np.array([[0],[1200]])\n",
        "# bottom right\n",
        "img1_pt4 = np.array([[812],[1200]])\n",
        "'''\n",
        "\n",
        "## image 1: The 4 corners of the input image: bigger input image: man-of-steel_small.jpg\n",
        "## point 1\n",
        "# top left\n",
        "img1_pt1 = np.array([[0],[0]])\n",
        "# top right\n",
        "img1_pt2 = np.array([[243],[0]])\n",
        "# bottom left\n",
        "img1_pt3 = np.array([[0],[360]])\n",
        "# bottom right\n",
        "img1_pt4 = np.array([[243],[360]])\n",
        "\n",
        "\n",
        "\n",
        "## image 2: The 4 corners of the Quadrilateral where the pixels inside would be replaced by the input pixels\n",
        "## image: horrorposter-preview_distorted.jpg\n",
        "# top left \n",
        "img2_pt1 = np.array([[486],[191]])\n",
        "# top right\n",
        "img2_pt2 = np.array([[780],[195]])\n",
        "# bottom left\n",
        "img2_pt3 = np.array([[378],[615]])\n",
        "# bottom right\n",
        "img2_pt4 = np.array([[670],[589]])\n",
        "\n",
        "# fill in Matrix A in AX=0 for estimating X        \n",
        "MatrixA.itemset((0,0),-img1_pt1.item(0,0))\n",
        "MatrixA.itemset((0,1),-img1_pt1.item(1,0))\n",
        "MatrixA.itemset((0,2),-1.0)\n",
        "MatrixA.itemset((0,3),0.0)\n",
        "MatrixA.itemset((0,4),0.0)\n",
        "MatrixA.itemset((0,5),0.0)\n",
        "MatrixA.itemset((0,6),img2_pt1.item(0,0)*img1_pt1.item(0,0))\n",
        "MatrixA.itemset((0,7),img2_pt1.item(0,0)*img1_pt1.item(1,0))\n",
        "MatrixA.itemset((0,8),img2_pt1.item(0,0))\n",
        "\n",
        "MatrixA.itemset((1,0),-img1_pt2.item(0,0))\n",
        "MatrixA.itemset((1,1),-img1_pt2.item(1,0))\n",
        "MatrixA.itemset((1,2),-1.0)\n",
        "MatrixA.itemset((1,3),0.0)\n",
        "MatrixA.itemset((1,4),0.0)\n",
        "MatrixA.itemset((1,5),0.0)\n",
        "MatrixA.itemset((1,6),img2_pt2.item(0,0)*img1_pt2.item(0,0))\n",
        "MatrixA.itemset((1,7),img2_pt2.item(0,0)*img1_pt2.item(1,0))\n",
        "MatrixA.itemset((1,8),img2_pt2.item(0,0))\n",
        "\n",
        "MatrixA.itemset((2,0),-img1_pt3.item(0,0))\n",
        "MatrixA.itemset((2,1),-img1_pt3.item(1,0))\n",
        "MatrixA.itemset((2,2),-1.0)\n",
        "MatrixA.itemset((2,3),0.0)\n",
        "MatrixA.itemset((2,4),0.0)\n",
        "MatrixA.itemset((2,5),0.0)\n",
        "MatrixA.itemset((2,6),img2_pt3.item(0,0)*img1_pt3.item(0,0))\n",
        "MatrixA.itemset((2,7),img2_pt3.item(0,0)*img1_pt3.item(1,0))\n",
        "MatrixA.itemset((2,8),img2_pt3.item(0,0))\n",
        "\n",
        "MatrixA.itemset((3,0),-img1_pt4.item(0,0))\n",
        "MatrixA.itemset((3,1),-img1_pt4.item(1,0))\n",
        "MatrixA.itemset((3,2),-1.0)\n",
        "MatrixA.itemset((3,3),0.0)\n",
        "MatrixA.itemset((3,4),0.0)\n",
        "MatrixA.itemset((3,5),0.0)\n",
        "MatrixA.itemset((3,6),img2_pt4.item(0,0)*img1_pt4.item(0,0))\n",
        "MatrixA.itemset((3,7),img2_pt4.item(0,0)*img1_pt4.item(1,0))\n",
        "MatrixA.itemset((3,8),img2_pt4.item(0,0))\n",
        "\n",
        "MatrixA.itemset((4,0),0.0)\n",
        "MatrixA.itemset((4,1),0.0)\n",
        "MatrixA.itemset((4,2),0.0)\n",
        "MatrixA.itemset((4,3),-img1_pt1.item(0,0))\n",
        "MatrixA.itemset((4,4),-img1_pt1.item(1,0))\n",
        "MatrixA.itemset((4,5),-1.0)\n",
        "MatrixA.itemset((4,6),img2_pt1.item(1,0)*img1_pt1.item(0,0))\n",
        "MatrixA.itemset((4,7),img2_pt1.item(1,0)*img1_pt1.item(1,0))\n",
        "MatrixA.itemset((4,8),img2_pt1.item(1,0))\n",
        "\n",
        "MatrixA.itemset((5,0),0.0)\n",
        "MatrixA.itemset((5,1),0.0)\n",
        "MatrixA.itemset((5,2),0.0)\n",
        "MatrixA.itemset((5,3),-img1_pt2.item(0,0))\n",
        "MatrixA.itemset((5,4),-img1_pt2.item(1,0))\n",
        "MatrixA.itemset((5,5),-1.0)\n",
        "MatrixA.itemset((5,6),img2_pt2.item(1,0)*img1_pt2.item(0,0))\n",
        "MatrixA.itemset((5,7),img2_pt2.item(1,0)*img1_pt2.item(1,0))\n",
        "MatrixA.itemset((5,8),img2_pt2.item(1,0))\n",
        "\n",
        "MatrixA.itemset((6,0),0.0)\n",
        "MatrixA.itemset((6,1),0.0)\n",
        "MatrixA.itemset((6,2),0.0)\n",
        "MatrixA.itemset((6,3),-img1_pt3.item(0,0))\n",
        "MatrixA.itemset((6,4),-img1_pt3.item(1,0))\n",
        "MatrixA.itemset((6,5),-1.0)\n",
        "MatrixA.itemset((6,6),img2_pt3.item(1,0)*img1_pt3.item(0,0))\n",
        "MatrixA.itemset((6,7),img2_pt3.item(1,0)*img1_pt3.item(1,0))\n",
        "MatrixA.itemset((6,8),img2_pt3.item(1,0))\n",
        "\n",
        "MatrixA.itemset((7,0),0.0)\n",
        "MatrixA.itemset((7,1),0.0)\n",
        "MatrixA.itemset((7,2),0.0)\n",
        "MatrixA.itemset((7,3),-img1_pt4.item(0,0))\n",
        "MatrixA.itemset((7,4),-img1_pt4.item(1,0))\n",
        "MatrixA.itemset((7,5),-1.0)\n",
        "MatrixA.itemset((7,6),img2_pt4.item(1,0)*img1_pt4.item(0,0))\n",
        "MatrixA.itemset((7,7),img2_pt4.item(1,0)*img1_pt4.item(1,0))\n",
        "MatrixA.itemset((7,8),img2_pt4.item(1,0))\n",
        "\n",
        "# performing SVD for estimating Homography matrix\n",
        "u, s, vh = np.linalg.svd(MatrixA, full_matrices=True)\n",
        "\n",
        "HomoMat.itemset((0,0),vh.item(8,0))\n",
        "HomoMat.itemset((0,1),vh.item(8,1))\n",
        "HomoMat.itemset((0,2),vh.item(8,2))\n",
        "\n",
        "HomoMat.itemset((1,0),vh.item(8,3))\n",
        "HomoMat.itemset((1,1),vh.item(8,4))\n",
        "HomoMat.itemset((1,2),vh.item(8,5))\n",
        "\n",
        "HomoMat.itemset((2,0),vh.item(8,6))\n",
        "HomoMat.itemset((2,1),vh.item(8,7))\n",
        "HomoMat.itemset((2,2),vh.item(8,8))\n",
        "\n",
        "\n",
        "\n",
        "def CoordinateTransformation(SimTranMax,y,x):\n",
        "    input_vector = np.array([[0],[0],[0]])\n",
        "    output_vector = np.array([[0],[0],[0]])\n",
        "    #print(type(output_vector))\n",
        "    \n",
        "    input_vector.itemset((0,0), x)\n",
        "    input_vector.itemset((1,0), y)\n",
        "    input_vector.itemset((2,0), 1.0)\n",
        "    \n",
        "    output_vector = np.matmul(SimTranMax,input_vector)\n",
        "    \n",
        "    output_vector.itemset((0,0), output_vector.item(0,0)/output_vector.item(2,0))\n",
        "    output_vector.itemset((1,0), output_vector.item(1,0)/output_vector.item(2,0))\n",
        "    return output_vector\n",
        "  \n",
        "  \n",
        "  \n",
        "def ImageTransformation(TranMax,src,result_img):\n",
        "    \n",
        "    h, w ,c = src.shape\n",
        "    # output image\n",
        "    #result_img = np.zeros_like(src)\n",
        "    \n",
        "    for i in range(h):\n",
        "        for j in range(w):\n",
        "        \n",
        "            pixel_R = src.item(i,j,0)\n",
        "            pixel_G = src.item(i,j,1)\n",
        "            pixel_B = src.item(i,j,2)           \n",
        "            \n",
        "            output_vector = CoordinateTransformation(TranMax,i,j)\n",
        "            \n",
        "            output_vector = output_vector.astype(int)\n",
        "            \n",
        "            output_vector_x = output_vector.item(0,0)\n",
        "            output_vector_y = output_vector.item(1,0)            \n",
        "        \n",
        "            result_img.itemset((output_vector_y,output_vector_x,0),pixel_R)\n",
        "            result_img.itemset((output_vector_y,output_vector_x,1),pixel_G)\n",
        "            result_img.itemset((output_vector_y,output_vector_x,2),pixel_B)\n",
        "            \n",
        "    return result_img\n",
        "  \n",
        "def InverseImageTransformation(SimTranMax_inv,src,result_img,img2_pt1,img2_pt2,img2_pt3,img2_pt4):\n",
        "    \n",
        "    h, w ,c = src.shape\n",
        "    # output image\n",
        "    #result_img = np.zeros_like(src)\n",
        "    top_y =  img2_pt1.item(1,0)\n",
        "    btm_y =  img2_pt4.item(1,0)\n",
        "    left_x = img2_pt1.item(0,0)\n",
        "    right_x =  img2_pt4.item(0,0)\n",
        "    \n",
        "    for i in range(top_y,btm_y):\n",
        "        for j in range(left_x, right_x):\n",
        "                                                                 \n",
        "            output_vector = CoordinateTransformation(SimTranMax_inv,i,j)\n",
        "            \n",
        "            output_vector = output_vector.astype(int)\n",
        "            \n",
        "            output_vector_x = output_vector.item(0,0)\n",
        "            output_vector_y = output_vector.item(1,0)            \n",
        "            \n",
        "            pixel_R = src.item(output_vector_y,output_vector_x,0)\n",
        "            pixel_G = src.item(output_vector_y,output_vector_x,1)\n",
        "            pixel_B = src.item(output_vector_y,output_vector_x,2)  \n",
        "            \n",
        "        \n",
        "            result_img.itemset((i,j,0),pixel_R)\n",
        "            result_img.itemset((i,j,1),pixel_G)\n",
        "            result_img.itemset((i,j,2),pixel_B)\n",
        "            \n",
        "    return result_img\n",
        "\n",
        "# 1st transformation:forward  \n",
        "result_img = ImageTransformation(HomoMat,img_rgb,img_des_rgb)\n",
        "\n",
        "# 2nd transformation:backward: won't work correctly in Homography. do you know why?\n",
        "#HomoMat_inv = np.linalg.inv(HomoMat)\n",
        "#result_img = InverseImageTransformation(HomoMat_inv,img_rgb,img_des_rgb,img2_pt1,img2_pt2,img2_pt3,img2_pt4)\n",
        "\n",
        "result_img_bgr = cv.cvtColor(result_img, cv.COLOR_RGB2BGR)\n",
        "\n",
        "cv2_imshow(result_img_bgr)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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        "id": "1RKtcLHvDxn3",
        "colab_type": "code",
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      "cell_type": "code",
      "source": [
        ""
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}