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Choose a method by data shape and goal
Smoothing may mean reducing noise in sampled values, blurring an image, or fitting a smooth approximation to observations. Interpolation is different: an interpolant passes through the supplied data points, while a smoothing fit may not. SciPy’s interpolation guide distinguishes structured, unstructured, and scattered data and notes that the appropriate routine depends on the data and the desired smoothness: SciPy interpolation guide.
| Data and goal | Candidate | Why it fits |
|---|---|---|
| Regularly spaced 1D samples; retain local polynomial shape or calculate derivatives | scipy.signal.savgol_filter |
Fits local polynomials across a moving window. |
| Image or other multidimensional array; blur at a chosen scale or calculate Gaussian derivatives | scipy.ndimage.gaussian_filter |
Applies a Gaussian filter, with scale selectable by axis. |
| 1D curve; balance closeness to observations against smoothness | Smoothing spline in scipy.interpolate |
Fits a smooth curve rather than applying a moving local filter. |
| Scattered or structured multidimensional data | Interpolation or fitting routine selected for the data geometry | The appropriate choice depends on whether the task is interpolation or approximation and on the arrangement of samples. |
These are method-selection distinctions, not claims that one method is universally faster or more accurate. Sampling assumptions also matter: SciPy’s signal-processing tutorial describes B-spline algorithms that assume equally spaced samples and mirror-symmetric boundary conditions: SciPy signal-processing tutorial.
Use Savitzky–Golay for local polynomial smoothing
scipy.signal.savgol_filter is a one-dimensional filter. For higher-rank arrays, it filters along one selected axis at a time; it does not automatically smooth every dimension. Choose a window length and polynomial degree that suit the local features you want to retain. The polynomial order must be less than the window length.
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from scipy.signal import savgol_filter
# y contains regularly spaced samples
smooth = savgol_filter(y, window_length= nine, polyorder=2)In runnable code, replace nine with an integer such as 9; the window length is a number of samples, not a duration. The example assumes the filtered axis contains at least nine values. The default mode='interp' fits edge polynomials and requires the window length not to exceed the input length along that axis. Specify axis if the samples are not on the default axis.
To estimate a derivative, set deriv to the derivative order. If sample spacing is not one unit, set delta to the spacing so derivative values use the appropriate scale. The default derivative order is zero, which returns smoothed values. See the savgol_filter API for parameter details and edge modes.
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Use a Gaussian filter for multidimensional arrays
scipy.ndimage.gaussian_filter is suited to images and other multidimensional arrays. Its sigma parameter is the Gaussian standard deviation; it may be a single value or a separate value for each axis. Per-axis values are useful when axis scales differ, though the values are expressed in array-index units unless the data have been appropriately scaled.
from scipy.ndimage import gaussian_filter
# Two-dimensional array: choose the blur scale for each axis
blurred = gaussian_filter(image, sigma=(1.0, 2.0), mode="reflect")Gaussian filtering uses order zero by default. A positive order selects a Gaussian derivative rather than ordinary smoothing. The default boundary mode is reflect, which mirrors values at the edge; boundary handling can affect results near array borders. Select a mode deliberately when edge values matter. Kernel support can be adjusted with truncate or, in supported API versions, radius. Consult the gaussian_filter API for the installed version’s exact parameter behavior.
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Use a smoothing spline when you need a fitted curve
A smoothing spline is a curve-fitting or approximation approach, not simply a moving filter. It trades closeness to observed points against smoothness; an interpolating spline, by contrast, passes through the supplied points. SciPy’s scipy.interpolate facilities include smoothing splines, generalized cross-validation options, knot-selection approaches, least-squares spline fitting, and two-dimensional smoothing surfaces. Choose among them according to data geometry and how much deviation from observations is acceptable. The interpolation guide explains the available approaches; verify the function names and signatures for the SciPy release used by your code.
Keep spline prefiltering distinct from smoothing
scipy.ndimage.spline_filter is a multidimensional spline filter used in spline interpolation workflows; it should not be treated as a general-purpose noise-removal function. Its intermediate arrays use the output data type, so limited precision can reduce accuracy. For precision-sensitive work, use a sufficiently high-precision output type. See the spline_filter API and the ndimage reference.
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Check these details before relying on a smoothed result
- Sampling: Determine whether observations are regularly spaced. Some signal-processing spline algorithms assume equally spaced samples.
- Edges: Decide how values beyond the array boundary should be handled. Edge rules can change filtered values near boundaries.
- Meaning of smooth: Choose between preserving local shape, blurring at a scale, and fitting a curve with a smoothness trade-off.
- Dimensions: Confirm the axis used by a one-dimensional filter or provide scale values appropriate to each Gaussian-filter axis.
- Version: Check the installed SciPy documentation for exact signatures and options, particularly when using newer spline or kernel-support parameters.
The official SciPy API documentation describes these functions and their parameters; it does not establish a universal performance winner or a single smoothing setting appropriate for all data.
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