{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"# The DCT (Discrete Cosine Transform)\n",
"\n",
"Jim Mahoney | Computer Science @ Marlboro College |\n",
"cs.marlboro.edu | Feb 2014 | MIT License\n",
"\n",
"An explanation and illustration of the math behind the Discrete Cosine Transform\n",
"and the concepts used in lossy JPEG image compression - low pass filtering."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The basic linear algebra with N = 2\n",
"\n",
"You can think of a vector - a list of numbers - as coefficients times basis vectors.\n",
"\n",
"$$ f_0 \\left[ \\begin{array}{c} 1 \\\\ 0 \\end{array} \\right] + f_1 \\left[ \\begin{array}{c} 0 \\\\ 1 \\end{array} \\right] $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using a different basis, different coefficients can describe the same vector.\n",
"\n",
"$$ G_0 \\frac{1}{\\sqrt{2}} \\left[ \\begin{array}{c} 1 \\\\ 1 \\end{array} \\right] + \n",
"G_1 \\frac{1}{\\sqrt{2}} \\left[ \\begin{array}{c} 1 \\\\ -1 \\end{array} \\right] $$\n",
"\n",
"(The sqrt(2)'s give the basis vectors length 1, i.e. \"normalizes\" them.)\n",
"\n",
"This transormation f to G is a DCT (Discrete Cosine Transform). \n",
"For a vector with 2 components, this perhaps isn't all that exciting, \n",
"but does still transform the original $(f_0, f_1)$ into low and high frequency components $(G_0, G_1)$.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### quick quiz 1\n",
"\n",
"If $f_0 = 3$ and $f_1 = 5$, what are the G's?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### the matrix math\n",
"\n",
"This transform can be written as a matrix multiplication.\n",
"\n",
"$$ \n",
"f_0 \\left[ \\begin{array}{c} 1 \\\\ 0 \\end{array} \\right] + f_1 \\left[ \\begin{array}{c} 0 \\\\ 1 \\end{array} \\right] = \n",
"\\left[ \\begin{array}{c} f_0 \\\\ f_1 \\end{array} \\right] = \n",
"G_0 \\frac{1}{\\sqrt{2}} \\left[ \\begin{array}{c} 1 \\\\ 1 \\end{array} \\right] + \n",
"G_1 \\frac{1}{\\sqrt{2}} \\left[ \\begin{array}{c} 1 \\\\ -1 \\end{array} \\right] =\n",
"\\frac{1}{\\sqrt{2}} \\left[ \\begin{array}{cc} 1 & 1 \\\\ 1 & -1 \\end{array} \\right] \n",
"\\left[ \\begin{array}{c} G_0 \\\\ G_1 \\end{array} \\right]\n",
"$$\n",
"\n",
"Moreover, this orthnormal matrix has the interesting and useful property that\n",
"its transpose is its inverse. That makes the equation easy to invert."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### quick quiz 2\n",
"\n",
"Show that the matrix times its transpose is the identity, and use that to find the G's."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### two dimensions\n",
"\n",
"The same idea can be applied to 2D images rather than 1D vectors,\n",
"by applying the 1D transform to each row and column of the image.\n",
"\n",
"The 2D basis images for N=2 are then the outer products of the 1D basis vectors.\n",
"From lowest (0,0) to highest (1,1) spatial frequency these basis images are :"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0, 0 :\n",
"[[ 0.5 0.5]\n",
" [ 0.5 0.5]]\n",
"\n",
"0, 1 :\n",
"[[ 0.5 -0.5]\n",
" [ 0.5 -0.5]]\n",
"\n",
"1, 0 :\n",
"[[ 0.5 0.5]\n",
" [-0.5 -0.5]]\n",
"\n",
"1, 1 :\n",
"[[ 0.5 -0.5]\n",
" [-0.5 0.5]]\n",
"\n"
]
}
],
"source": [
"basis = (1/sqrt(2) * array([1, 1]), 1/sqrt(2) * array([1, -1]))\n",
"for i in [0,1]:\n",
" for j in [0,1]:\n",
" print \"{}, {} :\".format(i,j)\n",
" print outer(basis[i], basis[j])\n",
" print\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### quick quiz\n",
"\n",
"For an image $ f = \\left[ \\begin{array}{cc} 5 & 8 \\\\ 4 & -1 \\end{array} \\right]$, what are the correspoding four $G$ coefficients?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## N = 8\n",
"\n",
"JPEG image compression uses the same sort of transform but with 8 coefficients, not 2.\n",
"\n",
"The matrix is defined by this formula :\n",
"\n",
"$$ \n",
"G_u = \\sqrt{\\frac{2}{N}} \\frac{1}{\\sqrt{2}} f_0 + \n",
"\\sqrt{\\frac{2}{N}} \\sum_{x=1}^7 f_x \\, cos\\left( \\frac{\\pi}{8} (u + \\frac{1}{2}) x \\right)\n",
"$$\n",
"\n",
"See http://en.wikipedia.org/wiki/Discrete_cosine_transform\n",
"and http://www.whydomath.org/node/wavlets/dct.html for the details.\n",
"In the wikipedia entry, we're using the JPEG transform which corresponds\n",
"to the \"Some authors further multiply the X0 term by 1/sqrt(2) and multiply the resulting matrix \n",
"by an overall scale factor of sqrt(2/N)\" variation, \n",
"where their $(k, n)$ indices are my $(u, x)$, \n",
"and their $(X_k, x_n)$ is my $(G_u, f_x)$.\n"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.354, 0.354, 0.354, 0.354, 0.354, 0.354, 0.354, 0.354],\n",
" [ 0.49 , 0.416, 0.278, 0.098, -0.098, -0.278, -0.416, -0.49 ],\n",
" [ 0.462, 0.191, -0.191, -0.462, -0.462, -0.191, 0.191, 0.462],\n",
" [ 0.416, -0.098, -0.49 , -0.278, 0.278, 0.49 , 0.098, -0.416],\n",
" [ 0.354, -0.354, -0.354, 0.354, 0.354, -0.354, -0.354, 0.354],\n",
" [ 0.278, -0.49 , 0.098, 0.416, -0.416, -0.098, 0.49 , -0.278],\n",
" [ 0.191, -0.462, 0.462, -0.191, -0.191, 0.462, -0.462, 0.191],\n",
" [ 0.098, -0.278, 0.416, -0.49 , 0.49 , -0.416, 0.278, -0.098]])"
]
},
"execution_count": 97,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The 8 x 8 DCT matrix thus looks like this.\n",
"N = 8\n",
"dct = zeros((N, N))\n",
"for x in range(N):\n",
" dct[0,x] = sqrt(2.0/N) / sqrt(2.0)\n",
"for u in xrange(1,N):\n",
" for x in xrange(N):\n",
" dct[u,x] = sqrt(2.0/N) * cos((pi/N) * u * (x + 0.5) )\n",
" \n",
"np.set_printoptions(precision=3)\n",
"dct"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The corresponding eight 1D basis vectors (the matrix rows) oscillate with successively higher spatial frequencies."
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiEAAALGCAYAAACTVkG9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Here's what they look like.\n",
"figure(figsize=(9,12))\n",
"for u in xrange(N):\n",
" subplot(4, 2, u+1)\n",
" ylim((-1, 1))\n",
" title(str(u))\n",
" plot(dct[u, :])\n",
" plot(dct[u, :],'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Like the N=2 case, the vectors are orthnormal. \n",
"In other words, their dot products are 0, and each has length 1. \n",
"Here are a few illustrative products."
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.99999999999999978,\n",
" 0.99999999999999989,\n",
" 5.5511151231257827e-17,\n",
" 1.9428902930940239e-16,\n",
" -2.4980018054066022e-16)"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def rowdot(i,j):\n",
" return dot(dct[i, :], dct[j, :])\n",
"rowdot(0,0), rowdot(3,3), rowdot(0,3), rowdot(1, 7), rowdot(1,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This also implies the inverse of this matrix is just its transpose."
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.354, 0.49 , 0.462, 0.416, 0.354, 0.278, 0.191, 0.098],\n",
" [ 0.354, 0.416, 0.191, -0.098, -0.354, -0.49 , -0.462, -0.278],\n",
" [ 0.354, 0.278, -0.191, -0.49 , -0.354, 0.098, 0.462, 0.416],\n",
" [ 0.354, 0.098, -0.462, -0.278, 0.354, 0.416, -0.191, -0.49 ],\n",
" [ 0.354, -0.098, -0.462, 0.278, 0.354, -0.416, -0.191, 0.49 ],\n",
" [ 0.354, -0.278, -0.191, 0.49 , -0.354, -0.098, 0.462, -0.416],\n",
" [ 0.354, -0.416, 0.191, 0.098, -0.354, 0.49 , -0.462, 0.278],\n",
" [ 0.354, -0.49 , 0.462, -0.416, 0.354, -0.278, 0.191, -0.098]])"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dct_transpose = dct.transpose()\n",
"dct_transpose"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 0., -0., 0., 0., 0., -0., -0.],\n",
" [ 0., 1., 0., -0., 0., -0., 0., 0.],\n",
" [-0., 0., 1., 0., -0., 0., 0., 0.],\n",
" [ 0., -0., 0., 1., 0., 0., -0., 0.],\n",
" [ 0., 0., -0., 0., 1., 0., -0., -0.],\n",
" [ 0., -0., 0., 0., 0., 1., 0., -0.],\n",
" [-0., 0., 0., -0., -0., 0., 1., 0.],\n",
" [-0., 0., 0., 0., -0., -0., 0., 1.]])"
]
},
"execution_count": 101,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Is the dot product of dct and its transpose the identity?\n",
"maybe_identity = dot(dct, dct_transpose)\n",
"\n",
"# Since there are many nearly zero like 3.2334e-17 in this numerical result,\n",
"# the output will look much nicer if we round them all of to (say) 6 places.\n",
"roundoff = vectorize(lambda m: round(m, 6))\n",
"roundoff(maybe_identity)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## playing with a real image\n",
"\n",
"To make all this more concrete, let's apply the 2D DCT transform to part of a real image.\n",
"\n",
"Here's one, takenly randomly from the web."
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAQIAAAD5CAYAAADMbTs+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLsUkmdG/plMAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# See http://matplotlib.org/users/image_tutorial.html for the image manipulation syntax.\n",
"# The image itself is a small piece from http://www.cordwainer-smith.com/virgil_finlay.htm.\n",
"import matplotlib.image as mpimg\n",
"img = mpimg.imread('stormplanet112.jpg')\n",
"p=plt.imshow(img, origin='lower')"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(112, 112, 3)"
]
},
"execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The image itself contains 3 dimensions: rows, columns, and colors\n",
"img.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All three of the R,G,B color values in the greyscale image are the same for each pixel.\n",
"\n",
"Let's just look at values from one tiny 8 x 8 block (which is what's used JPEG compression) near his nose.\n",
"\n",
"(The next images use a false color spectrum to display pixel intensity.)"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAASgAAAD5CAYAAACUEqgnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tiny = img[40:48, 40:48, 0] # a tiny 8 x 8 block, in the color=0 (Red) channel\n",
"\n",
"def show_image(img):\n",
" plt.imshow(img)\n",
" plt.colorbar()\n",
"\n",
"show_image(tiny)"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 24, 147, 212, 216, 209, 223, 156, 74],\n",
" [ 47, 33, 179, 221, 201, 230, 164, 95],\n",
" [ 20, 73, 201, 235, 215, 219, 175, 109],\n",
" [140, 181, 215, 217, 197, 192, 142, 95],\n",
" [204, 235, 206, 195, 204, 208, 192, 159],\n",
" [208, 187, 217, 226, 222, 216, 209, 173],\n",
" [203, 234, 225, 211, 204, 185, 232, 227],\n",
" [155, 143, 150, 193, 204, 177, 178, 195]], dtype=uint8)"
]
},
"execution_count": 105,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# And here are the numbers.\n",
"tiny"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we define the 2D version of the N=8 DCT described above. \n",
"\n",
"The trick is to apply the 1D DCT to every column, *and* then also apply it to every row, i.e.\n",
"\n",
"$$ G = {DCT} \\cdot f \\cdot {DCT}^{T} $$"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAASgAAAD5CAYAAACUEqgnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def doDCT(grid):\n",
" return dot(dot(dct, grid), dct_transpose)\n",
"\n",
"def undoDCT(grid):\n",
" return dot(dot(dct_transpose, grid), dct)\n",
"\n",
"# test : do DCT, then undo DCT; should get back the same image.\n",
"tiny_do_undo = undoDCT(doDCT(tiny))\n",
"\n",
"show_image(tiny_do_undo) # Yup, looks the same."
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 24., 147., 212., 216., 209., 223., 156., 74.],\n",
" [ 47., 33., 179., 221., 201., 230., 164., 95.],\n",
" [ 20., 73., 201., 235., 215., 219., 175., 109.],\n",
" [ 140., 181., 215., 217., 197., 192., 142., 95.],\n",
" [ 204., 235., 206., 195., 204., 208., 192., 159.],\n",
" [ 208., 187., 217., 226., 222., 216., 209., 173.],\n",
" [ 203., 234., 225., 211., 204., 185., 232., 227.],\n",
" [ 155., 143., 150., 193., 204., 177., 178., 195.]])"
]
},
"execution_count": 115,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# And the numbers are the same.\n",
"tiny_do_undo"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The DCT transform looks like this. \n",
"Note that most of the intensity is at the top left, in the lowest frequencies."
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAATAAAAD5CAYAAACga2k7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvmwAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tinyDCT = doDCT(tiny)\n",
"show_image(tinyDCT)"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([['1429.2', ' -55.9', '-241.7', ' -9.0', ' -54.7', ' 31.9', ' 9.7', ' 0.1'],\n",
" ['-152.3', ' -58.3', '-201.2', ' -4.0', ' -64.9', ' 24.0', ' 35.8', ' -10.9'],\n",
" [' -54.2', ' -74.9', ' -27.0', ' -15.7', ' 8.3', ' -0.2', ' 0.1', ' 0.3'],\n",
" [' 92.6', ' 59.6', ' 48.2', ' 12.2', ' -30.1', ' -17.3', ' -16.2', ' 0.1'],\n",
" [' -19.7', ' 64.2', ' 21.0', ' 10.9', ' -14.3', ' -44.2', ' -21.1', ' -15.0'],\n",
" [' 35.3', ' 41.9', ' 0.2', ' -39.1', ' -32.3', ' -21.0', ' -23.1', ' 0.2'],\n",
" [' -19.8', ' -26.2', ' -47.4', ' -0.7', ' 0.4', ' 0.3', ' 0.5', ' -0.3'],\n",
" [' 27.9', ' -18.2', ' 19.1', ' -20.5', ' -22.5', ' -20.0', ' -21.1', ' 0.7']], \n",
" dtype='|S8')"
]
},
"execution_count": 109,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"set_printoptions(linewidth=100) # output line width (default is 75)\n",
"round6 = vectorize(lambda m: '{:6.1f}'.format(m))\n",
"round6(tinyDCT)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"The grid positions in that last image correspond to spatial frequencies, with the lowest DC component at the top left, and the highest vertical and horizontal frequency at the bottom right.\n",
"\n",
"These 2D basis functions can be visualized with this image from wikimedia commons."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The details of what I'm doing here don't really match the JPEG transformations:\n",
"I haven't done the color space transforms, and I haven't handled the DC offsets\n",
"as the JPEG spec does (which centers the values around 0 explicitly.)\n",
"\n",
"But the concept is visible in the last two pictures: after the DCT, most of the power is in fewer pixels, which are typically near the top left DC part of the grid. \n",
"\n",
"So here's a simple lossy \"low pass filter\" of the data : let's \n",
"chop some of the high frequency numbers.\n",
"One (somewhat arbitrary) choice to to set the frequencies \n",
"higher than the (1,7) to (7,1) line, to zero.\n",
"\n",
"This is a lossy transormation since we're throwing away information - \n",
"it can't be undone. But since there are fewer numbers, it's a form \n",
"of compression."
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAATAAAAD5CAYAAACga2k7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# First make a copy to work on.\n",
"tinyDCT_chopped = tinyDCT.copy()\n",
"\n",
"# Then zero the pieces below the x + y = 8 line.\n",
"for x in xrange(N):\n",
" for u in xrange(N):\n",
" if x + u > 8:\n",
" tinyDCT_chopped[x,u] = 0.0\n",
"\n",
"show_image(tinyDCT_chopped)"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([['1429.2', ' -55.9', '-241.7', ' -9.0', ' -54.7', ' 31.9', ' 9.7', ' 0.1'],\n",
" ['-152.3', ' -58.3', '-201.2', ' -4.0', ' -64.9', ' 24.0', ' 35.8', ' -10.9'],\n",
" [' -54.2', ' -74.9', ' -27.0', ' -15.7', ' 8.3', ' -0.2', ' 0.1', ' 0.0'],\n",
" [' 92.6', ' 59.6', ' 48.2', ' 12.2', ' -30.1', ' -17.3', ' 0.0', ' 0.0'],\n",
" [' -19.7', ' 64.2', ' 21.0', ' 10.9', ' -14.3', ' 0.0', ' 0.0', ' 0.0'],\n",
" [' 35.3', ' 41.9', ' 0.2', ' -39.1', ' 0.0', ' 0.0', ' 0.0', ' 0.0'],\n",
" [' -19.8', ' -26.2', ' -47.4', ' 0.0', ' 0.0', ' 0.0', ' 0.0', ' 0.0'],\n",
" [' 27.9', ' -18.2', ' 0.0', ' 0.0', ' 0.0', ' 0.0', ' 0.0', ' 0.0']], \n",
" dtype='|S8')"
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"round6(tinyDCT_chopped)\n",
"# Notice all the zeros at the bottom right - those are the chopped high frequences.\n",
"# We've essentially done a \"low pass filter\" on the spacial frequencies."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see what this did to the original, we just transform it back."
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAASgAAAD5CAYAAACUEqgnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tiny_chopped_float = undoDCT(tinyDCT_chopped)\n",
"\n",
"# Also convert the floats back to uint8, which was the original format\n",
"tiny_chopped = vectorize(lambda x: uint8(x))(tiny_chopped_float) \n",
"\n",
"show_image(tiny_chopped)"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 39, 119, 222, 223, 202, 226, 154, 73],\n",
" [ 25, 71, 171, 206, 204, 226, 167, 96],\n",
" [ 21, 72, 188, 241, 225, 221, 168, 107],\n",
" [146, 173, 222, 219, 186, 181, 149, 100],\n",
" [210, 217, 213, 197, 203, 217, 195, 147],\n",
" [193, 212, 214, 213, 222, 214, 205, 181],\n",
" [212, 220, 218, 220, 210, 188, 216, 232],\n",
" [152, 145, 153, 190, 199, 173, 191, 188]], dtype=uint8)"
]
},
"execution_count": 118,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tiny_chopped"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we have something close to the original back again - even though close to half of the transformed image was set to zero."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## conclusions\n",
"\n",
"The procedue here isn't what happens in JPEG compression, but does illustrate one of the central \n",
"concepts - throwing away some of higher spatial frequency information after a DCT transform.\n",
"\n",
"In the real JPEG lossy compression algorithm, the steps are\n",
"\n",
"* the color space is transformed from R,G,B to Y,Cb,Cr to take advantage of human visual prejudices\n",
"\n",
"* the values are shifted so that they center around zero\n",
"\n",
"* the values after the DCT are \"quantized\" (i.e. rounded off) by different amounts at different spots in the grid. *(*This* is the lossy step, and how lossy depends on the JPEG quality.)\n",
"\n",
"* a zigzag (keeping similar frequencies together) pattern turns this to a 1D stream of 64 values\n",
"\n",
"* which are then huffman encoded by, typically by a pre-chosen code (part of the JPEG standard)\n",
"\n",
"For all the JPEG details, see http://en.wikipedia.org/wiki/JPEG .\n"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.1"
}
},
"nbformat": 4,
"nbformat_minor": 1
}