threeStage | R Documentation |

Estimate jump location curves using local principal component lines. One-sided kernel smoothing is then used for surface estimation. Bandwidth is specified by the user.

```
threeStage(image, bandwidth, edge1, edge2,
blur = FALSE, plot = FALSE)
```

`image` |
A square matrix, no missing value allowed. |

`bandwidth` |
A positive integer that specifies the number of pixels to use in the local smoothing. |

`edge1` |
A matrix of 0 and 1 representing the detected step edge pixels |

`edge2` |
A matrix of 0 and 1 representing the detected roof/valley edge pixels |

`blur` |
If blur = TRUE, besides a conventional 2-D kernel function, a univariate increasing kernel function is used in the local kernel smoothing to address the issue with blur. |

`plot` |
If plot = TRUE, the image of the fitted surface is plotted |

At each pixel, if there are step edges detected in the local neighborhood, a principal component line is fitted through the detected edge pixels to approximate the step edge locally and then the regression surface is estimated by a local constant kernel smoothing procedure using only the pixels on one side of the principal component line. If there are no step edges but roof/valley edges detected in the local neighborhood, the same procedure is followed except that the principal component line to fitted through the detected roof/valley edge pixels. In cases when there is either no step edges or roof/valley edges detected in the neighborhood, the regression surface at the pixel is estimated by the conventional local linear kernel smoothing procedure.

The restored image, which is represented by a matrix.

Qiu, P. and Kang, Y. (2015) “Blind Image Deblurring Using Jump
Regression Analysis”, *Statistica Sinica*, **25**,
879 – 899, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.5705/ss.2014.054")}.

`JPLLK_surface`

, `surfaceCluster`

```
step.edges <- stepEdge(sar, bandwidth = 4, thresh = 20, degree = 0)
stepEdge1 <- modify2(bandwidth = 4, step.edges)
fit <- threeStage(image = sar, bandwidth = 4, edge1 = stepEdge1,
edge2 = array(0, rep(ncol(sar), 2)))
```

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