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  • 101-analyzing-the-frequency-components-of-a-signal-with-a-fast-fourier-transform
  • 102-applying-a-linear-filter-to-a-digital-signal
  • 103-computing-the-autocorrelation-of-a-time-series
  • 11-introducing-ipython-and-the-jupyter-notebook
  • 111-manipulating-the-exposure-of-an-image
  • 112-applying-filters-on-an-image
  • 113-segmenting-an-image
  • 114-finding-points-of-interest-in-an-image
  • 115-detecting-faces-in-an-image-with-opencv
  • 116-applying-digital-filters-to-speech-sounds
  • 117-creating-a-sound-synthesizer-in-the-notebook
  • 12-getting-started-with-exploratory-data-analysis-in-the-jupyter-notebook
  • 121-plotting-the-bifurcation-diagram-of-a-chaotic-dynamical-system
  • 122-simulating-an-elementary-cellular-automaton
  • 123-simulating-an-ordinary-differential-equation-with-scipy
  • 124-simulating-a-partial-differential-equation-reaction-diffusion-systems-and-turing-patterns
  • 13-introducing-the-multidimensional-array-in-numpy-for-fast-array-computations
  • 131-simulating-a-discrete-time-markov-chain
  • 132-simulating-a-poisson-process
  • 133-simulating-a-brownian-motion
  • 134-simulating-a-stochastic-differential-equation
  • 14-creating-an-ipython-extension-with-custom-magic-commands
  • 141-manipulating-and-visualizing-graphs-with-networkx
  • 142-drawing-flight-routes-with-networkx
  • 143-resolving-dependencies-in-a-directed-acyclic-graph-with-a-topological-sort
  • 144-computing-connected-components-in-an-image
  • 145-computing-the-voronoi-diagram-of-a-set-of-points
  • 146-manipulating-geospatial-data-with-cartopy
  • 147-creating-a-route-planner-for-a-road-network
  • 15-mastering-ipythons-configuration-system
  • 151-diving-into-symbolic-computing-with-sympy
  • 152-solving-equations-and-inequalities
  • 153-analyzing-real-valued-functions
  • 154-computing-exact-probabilities-and-manipulating-random-variables
  • 155-a-bit-of-number-theory-with-sympy
  • 156-finding-a-boolean-propositional-formula-from-a-truth-table
  • 157-analyzing-a-nonlinear-differential-system-lotka-volterra-predator-prey-equations
  • 158-getting-started-with-sage
  • 16-creating-a-simple-kernel-for-jupyter
  • 21-learning-the-basics-of-the-unix-shell
  • 22-using-the-latest-features-of-python-3
  • 23-learning-the-basics-of-the-distributed-version-control-system-git
  • 24-a-typical-workflow-with-git-branching
  • 25-efficient-interactive-computing-workflows-with-ipython
  • 26-ten-tips-for-conducting-reproducible-interactive-computing-experiments
  • 27-writing-high-quality-python-code
  • 28-writing-unit-tests-with-pytest
  • 29-debugging-code-with-ipython
  • 31-teaching-programming-in-the-notebook-with-ipython-blocks
  • 32-converting-a-jupyter-notebook-to-other-formats-with-nbconvert
  • 33-mastering-widgets-in-the-jupyter-notebook
  • 34-creating-custom-jupyter-notebook-widgets-in-python-html-and-javascript
  • 35-configuring-the-jupyter-notebook
  • 36-introducing-jupyterlab
  • 404.html
  • 41-evaluating-the-time-taken-by-a-command-in-ipython
  • 42-profiling-your-code-easily-with-cprofile-and-ipython
  • 43-profiling-your-code-line-by-line-with-line_profiler
  • 44-profiling-the-memory-usage-of-your-code-with-memory_profiler
  • 45-understanding-the-internals-of-numpy-to-avoid-unnecessary-array-copying
  • 46-using-stride-tricks-with-numpy
  • 47-implementing-an-efficient-rolling-average-algorithm-with-stride-tricks
  • 48-processing-large-numpy-arrays-with-memory-mapping
  • 49-manipulating-large-arrays-with-hdf5
  • 51-knowing-python-to-write-faster-code
  • 510-interacting-with-asynchronous-parallel-tasks-in-ipython
  • 511-performing-out-of-core-computations-on-large-arrays-with-dask
  • 512-trying-the-julia-programming-language-in-the-jupyter-notebook
  • 52-accelerating-pure-python-code-with-numba-and-just-in-time-compilation
  • 53-accelerating-array-computations-with-numexpr
  • 54-wrapping-a-c-library-in-python-with-ctypes
  • 55-accelerating-python-code-with-cython
  • 56-optimizing-cython-code-by-writing-less-python-and-more-c
  • 57-releasing-the-gil-to-take-advantage-of-multi-core-processors-with-cython-and-openmp
  • 58-writing-massively-parallel-code-for-nvidia-graphics-cards-gpus-with-cuda
  • 59-distributing-python-code-across-multiple-cores-with-ipython
  • 61-using-matplotlib-styles
  • 62-creating-statistical-plots-easily-with-seaborn
  • 63-creating-interactive-web-visualizations-with-bokeh-and-holoviews
  • 64-visualizing-a-networkx-graph-in-the-notebook-with-d3js
  • 65-discovering-interactive-visualization-libraries-in-the-notebook
  • 66-creating-plots-with-altair-and-the-vega-lite-specification
  • 71-exploring-a-dataset-with-pandas-and-matplotlib
  • 72-getting-started-with-statistical-hypothesis-testing-a-simple-z-test
  • 73-getting-started-with-bayesian-methods
  • 74-estimating-the-correlation-between-two-variables-with-a-contingency-table-and-a-chi-squared-test
  • 75-fitting-a-probability-distribution-to-data-with-the-maximum-likelihood-method
  • 76-estimating-a-probability-distribution-nonparametrically-with-a-kernel-density-estimation
  • 77-fitting-a-bayesian-model-by-sampling-from-a-posterior-distribution-with-a-markov-chain-monte-carlo-method
  • 78-analyzing-data-with-the-r-programming-language-in-the-jupyter-notebook
  • 81-getting-started-with-scikit-learn
  • 82-predicting-who-will-survive-on-the-titanic-with-logistic-regression
  • 83-learning-to-recognize-handwritten-digits-with-a-k-nearest-neighbors-classifier
  • 84-learning-from-text-naive-bayes-for-natural-language-processing
  • 85-using-support-vector-machines-for-classification-tasks
  • 86-using-a-random-forest-to-select-important-features-for-regression
  • 87-reducing-the-dimensionality-of-a-dataset-with-a-principal-component-analysis
  • 88-detecting-hidden-structures-in-a-dataset-with-clustering
  • 91-finding-the-root-of-a-mathematical-function
  • 92-minimizing-a-mathematical-function
  • 93-fitting-a-function-to-data-with-nonlinear-least-squares
  • 94-finding-the-equilibrium-state-of-a-physical-system-by-minimizing-its-potential-energy
  • archives.html
  • authors.html
  • categories.html
  • chapter-1-a-tour-of-interactive-computing-with-jupyter-and-ipython
  • chapter-10-signal-processing
  • chapter-11-image-and-audio-processing
  • chapter-12-deterministic-dynamical-systems
  • chapter-13-stochastic-dynamical-systems
  • chapter-14-graphs-geometry-and-geographic-information-systems
  • chapter-15-symbolic-and-numerical-mathematics
  • chapter-2-best-practices-in-interactive-computing
  • chapter-3-mastering-the-jupyter-notebook
  • chapter-4-profiling-and-optimization
  • chapter-5-high-performance-computing
  • chapter-6-data-visualization
  • chapter-7-statistical-data-analysis
  • chapter-8-machine-learning
  • chapter-9-numerical-optimization
  • cookbook
  • feeds
  • index.html
  • minibook
  • pages
  • tags.html

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‎101-analyzing-the-frequency-components-of-a-signal-with-a-fast-fourier-transform/index.html

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‎102-applying-a-linear-filter-to-a-digital-signal/index.html

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<p>scikit-image should be included by default in Anaconda. Otherwise, you can always install it manually with <code>conda install scikit-image</code>.</p>
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<h2>How to do it...</h2>
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<p><strong>1.&nbsp;</strong> Let's import the packages:</p>
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<div class="highlight highlight-python"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
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<div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
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<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
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<span class="kn">import</span> <span class="nn">skimage.exposure</span> <span class="kn">as</span> <span class="nn">skie</span>
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<span class="o">%</span><span class="n">matplotlib</span> <span class="n">inline</span>
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<p><strong>2.&nbsp;</strong> We open an image with matplotlib. We only take a single RGB component to have a grayscale image (it is a very crude way of doing it, we give much better ways at the end of this recipe):</p>
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<div class="highlight highlight-python"><div class="highlight"><pre><span></span><span class="n">img</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">imread</span><span class="p">(</span><span class="s1">&#39;https://github.com/ipython-books/&#39;</span>
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<div class="highlight"><pre><span></span><span class="n">img</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">imread</span><span class="p">(</span><span class="s1">&#39;https://github.com/ipython-books/&#39;</span>
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<span class="s1">&#39;cookbook-2nd-data/blob/master/&#39;</span>
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<span class="s1">&#39;beach.png?raw=true&#39;</span><span class="p">)[</span><span class="o">...</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
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<p><strong>3.&nbsp;</strong> We create a function that displays the image along with its <strong>histogram</strong> of the intensity values (that is, the exposure):</p>
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<div class="highlight highlight-python"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">show</span><span class="p">(</span><span class="n">img</span><span class="p">):</span>
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<div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">show</span><span class="p">(</span><span class="n">img</span><span class="p">):</span>
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<span class="c1"># Display the image.</span>
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<span class="n">fig</span><span class="p">,</span> <span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">)</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span>
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<span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<p><strong>4.&nbsp;</strong> Let's display the image along with its histogram:</p>
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<div class="highlight"><pre><span></span><span class="n">show</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
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<p><img alt="&lt;matplotlib.figure.Figure at 0x7795080&gt;" src="http://ipython-books.github.io/pages/chapter11_image/01_exposure_files/01_exposure_12_0.png" /></p>
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<p>The histogram is unbalanced and the image appears overexposed (many pixels are too bright).</p>
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<p><strong>5.&nbsp;</strong> Now, we rescale the intensity of the image using scikit-image's <code>rescale_intensity</code> function. The <code>in_range</code> and <code>out_range</code> parameters define a linear mapping from the original image to the modified image. The pixels that are outside <code>in_range</code> are clipped to the extremal values of <code>out_range</code>. Here, the darkest pixels (intensity less than 100) become completely black (0), whereas the brightest pixels (&gt;240) become completely white (255):</p>
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<div class="highlight"><pre><span></span><span class="n">show</span><span class="p">(</span><span class="n">skie</span><span class="o">.</span><span class="n">rescale_intensity</span><span class="p">(</span>
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<span class="n">img</span><span class="p">,</span> <span class="n">in_range</span><span class="o">=</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="o">.</span><span class="mi">95</span><span class="p">),</span> <span class="n">out_range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)))</span>
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<p><img alt="A crude exposure manipulation technique" src="http://ipython-books.github.io/pages/chapter11_image/01_exposure_files/01_exposure_15_0.png" /></p>
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<p>Many intensity values seem to be missing in the histogram, which reflects the poor quality of this crude exposure correction technique.</p>
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<p><strong>6.&nbsp;</strong> We now use a more advanced exposure correction technique called <strong>Contrast Limited Adaptive Histogram Equalization (CLAHE)</strong>:</p>
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<div class="highlight highlight-python"><div class="highlight"><pre><span></span><span class="n">show</span><span class="p">(</span><span class="n">skie</span><span class="o">.</span><span class="n">equalize_adapthist</span><span class="p">(</span><span class="n">img</span><span class="p">))</span>
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<div class="highlight"><pre><span></span><span class="n">show</span><span class="p">(</span><span class="n">skie</span><span class="o">.</span><span class="n">equalize_adapthist</span><span class="p">(</span><span class="n">img</span><span class="p">))</span>
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<p><img alt="&lt;matplotlib.figure.Figure at 0x7ade080&gt;" src="http://ipython-books.github.io/pages/chapter11_image/01_exposure_files/01_exposure_18_1.png" /></p>
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