- Digital Image Processing
- DIP - Home
- DIP - Image Processing Introduction
- DIP - Signal and System Introduction
- DIP - History of Photography
- DIP - Applications and Usage
- DIP - Concept of Dimensions
- DIP - Image Formation on Camera
- DIP - Camera Mechanism
- DIP - Concept of Pixel
- DIP - Perspective Transformation
- DIP - Concept of Bits Per Pixel
- DIP - Types of Images
- DIP - Color Codes Conversion
- DIP - Grayscale to RGB Conversion
- DIP - Concept of Sampling
- DIP - Pixel Resolution
- DIP - Concept of Zooming
- DIP - Zooming methods
- DIP - Spatial Resolution
- DIP - Pixels Dots and Lines per inch
- DIP - Gray Level Resolution
- DIP - Concept of Quantization
- DIP - ISO Preference curves
- DIP - Concept of Dithering
- DIP - Histograms Introduction
- DIP - Brightness and Contrast
- DIP - Image Transformations
- DIP - Histogram Sliding
- DIP - Histogram Stretching
- DIP - Introduction to Probability
- DIP - Histogram Equalization
- DIP - Gray Level Transformations
- DIP - Concept of convolution
- DIP - Concept of Masks
- DIP - Concept of Blurring
- DIP - Concept of Edge Detection
- DIP - Prewitt Operator
- DIP - Sobel operator
- DIP - Robinson Compass Mask
- DIP - Krisch Compass Mask
- DIP - Laplacian Operator
- DIP - Frequency Domain Analysis
- DIP - Fourier series and Transform
- DIP - Convolution theorm
- DIP - High Pass vs Low Pass Filters
- DIP - Introduction to Color Spaces
- DIP - JPEG compression
- DIP - Optical Character Recognition
- DIP - Computer Vision and Graphics

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# Laplacian Operator

Laplacian Operator is also a derivative operator which is used to find edges in an image. The major difference between Laplacian and other operators like Prewitt, Sobel, Robinson and Kirsch is that these all are first order derivative masks but Laplacian is a second order derivative mask. In this mask we have two further classifications one is Positive Laplacian Operator and other is Negative Laplacian Operator.

Another difference between Laplacian and other operators is that unlike other operators Laplacian didn’t take out edges in any particular direction but it take out edges in following classification.

- Inward Edges
- Outward Edges

Let’s see that how Laplacian operator works.

## Positive Laplacian Operator

In Positive Laplacian we have standard mask in which center element of the mask should be negative and corner elements of mask should be zero.

0 | 1 | 0 |

1 | -4 | 1 |

0 | 1 | 0 |

Positive Laplacian Operator is use to take out outward edges in an image.

## Negative Laplacian Operator

In negative Laplacian operator we also have a standard mask, in which center element should be positive. All the elements in the corner should be zero and rest of all the elements in the mask should be -1.

0 | -1 | 0 |

-1 | 4 | -1 |

0 | -1 | 0 |

Negative Laplacian operator is use to take out inward edges in an image

### How it works

Laplacian is a derivative operator; its uses highlight gray level discontinuities in an image and try to deemphasize regions with slowly varying gray levels. This operation in result produces such images which have grayish edge lines and other discontinuities on a dark background. This produces inward and outward edges in an image

The important thing is how to apply these filters onto image. Remember we can’t apply both the positive and negative Laplacian operator on the same image. we have to apply just one but the thing to remember is that if we apply positive Laplacian operator on the image then we subtract the resultant image from the original image to get the sharpened image. Similarly if we apply negative Laplacian operator then we have to add the resultant image onto original image to get the sharpened image.

Let’s apply these filters onto an image and see how it will get us inward and outward edges from an image. Suppose we have a following sample image.

### Sample Image

### After applying Positive Laplacian Operator

After applying positive Laplacian operator we will get the following image.

### After applying Negative Laplacian Operator

After applying negative Laplacian operator we will get the following image.