Image enhancement Antti Tuomas Jalava Jaime Garrido Ceca
Overview • Digital subtraction angiography. Dual-energy and energy-subtraction X-ray imaging. Temporal subtraction. • Gray-scale transform. • Convolution mask operators. • High-frequency enhancement. • Adaptive contrast enhancement. • Objective assessment of Contrast Enhancement.
Digital Subtraction Angiography PROCESS : • Agent is injected to increase the density of the blood • Number of X-ray images. • An image taken before the injection of the agent is used as the mask or reference image. • Subtracted from the “live” images to obtain enhanced images. • Useful to detect sclerosis. • The mathematical procedure involved may be expressed simply as: • Sensitive to motion
Dual-energy and Energy-subtraction X-ray Imaging • X-ray images at multiple energy levels • Distribution of specific materials in the object or body imaged • Weighted combinations of multiple-energy images • soft-tissue and hard tissue separately
Temporal Subtraction • To detect normal or pathological changes occurred over a period of time. • Detection of lung nodules • Normal anatomic structures are suppressed and pathological are enhanced.
Gray Scale TransformOverview • Gray-scale thresholding. • Gray-scale windowing. • Gamma correction. • Histogram transformation. • Histogram specification. • Limitation of global operations. • Local-area histogram equalization. • Adaptive-neighborhood histogram equalization.
Gray-scale Transforms (I) • Presence of different levels of density or intensity in the image. • Histogram gray-scale transform. • Improve the visibility of details.
Gray-scale Transforms (II) • Gray-scale thresholding. • Gray level object > L new bi-level image. Problem: Narrow range of gray levels. Solution: Stretch the range of interest to the full range. • Gray-scale windowing. • Linear transformation • Gamma correction. • Non-linear transformations
Original image L = 30 New Image Thresholding
Original image γ = 0.3 New image Gamma Correction
Original image New image f1 = 5 f2 = 60 Windowing
Histogram Transformation • Principle: maximal information is conveyed when PDF is uniform. • Histogram transformation is used to enhance the image. • Histogram-based methods: • Histogram equalization. • Histogram specification. • Local-area histogram equalization (LAHE). • Adaptive-neighborhood histogram equalization.
Histogram Equalization • Goal: • Discrete version: • Properties of this function: • Single value monotonically increasing. • Maintain same range of values.
Original image Equalized image
Histogram of the original image Equalized Histogram
Histogram Specification • Problem: H. Equalization provides only one output image. Not satisfactory in many cases. • Histogram Specification is a series of histogram-equalization steps to obtain prespecified histogram. Process: • Specify the desired histogram and derive • Derive the histogram-equalizing transform • Derive from • Obtain • Transform to image f.
Limitations of Global Operations • Global operators (Gray-scale & histogram transform) provides simple mechanisms to manipulate the image. • Global approach to image enhancement ignores the nonstationary nature of images. • Given wide range of details of interest in medical image, such as hard and soft tissues, it is desirable to design local and adaptive transform for effective image enhancement.
Local-area Histogram Equalization (LAHE) • Problem: Gray levels with low probability are merged upon quantization of the equalizing transform lost in the enhanced image. • 2D sliding window. • Resulting transform is applied only to the central pixel. • Computationally expensive. • LAHE variation: • Not every pixel. Only nonoverlapping rectangular block spanning the image.
Adaptive-neighborhood Histogram Equalization • Limitation of LAHE: no justification to the choice of the rectangular shape and the size of the window. • Identification of shape and size neighborhoods for each pixel by region growing. • Uniform region spans a limited range of gray levels by a specified threshold. • Local area composed not only by foreground region growing but also by background one. • Histogram of the local region equalizing transform to the seed pixel and all the pixels with the same value.
Adaptive-neighborhood Histogram Equalization Original Equalization, Background depth 5, growth threshold 16
Convolution Mask Operators for Image Enhancement • 2D convolution of images with 3 x 3 masks. • Unsharp masking • Subtraction Laplacian
Convolution Mask OperatorsUnsharp Masking • Tackles blurring by an unknown phenomenon. • Assumes that each pixel of original image contributes also to neighboring pixels. • Results into a fog. • Procedure: • The original degraded image is blurred. • The blurred image is subtracted from the degraded image. • Removes the fog. • General form: Where is local mean in degraded image . Mean filter Unsharp mask
Convolution Mask OperatorsSubtraction Laplacian • Assumption that degraded image is a result of diffusion process that spreads intensity values over space as a function of time • 3 x 3 convolution mask form of Laplacian (gradient): • With weighting factor set to 1 the subtraction Laplacian is:
Convolution Mask OperatorsProblems • Edge enhancement & high-frequency emphasis (Over and under-shoot seen as halos around edges). • While seeming sharper, some finer details might be lost. • Can lead to negative pixel values. • Linear mapping back to display range can cancel any enhancing. • Fixed operators. • No adaptivity to variability within image.
Unsharp mask, A = 1, B = 9, Normalized dynamic range Original Unsharp mask, A = 1, B = 9, Dynamic range cut to original Subtracting Laplacian, A = 1, B = 5, Normalized dynamic range
High-frequency Emphasis • Bad idea: Ideal highpass filter • Introduces ringing artifacts. • Butterworth highpass filter • Use of smooth transition from stopband to pass band. • Artifact reduction. • Extracts only edges. • Order n. • Butterworth high-emphasis filter • Adds constant to frequency space. • Preserves image and sharpens edges.
Homomorphic Filtering (I) • Already known: Two images with different frequency composition that are added together can be separated with linear filtering. • Two images multiplied with each other? • Take logarithm first. (subscript l indicates that Fourier transform has been applied to Fourier transformed image) • Then filter, inverse Fourier transform and reverse logarithm with exponent.
Homomorphic Filtering (II) • Extension for convolved images (Chapter 10.3). • generalized linear filtering. • Operations are called homomorphic systems. • With highpass filter used to achieve simultaneous dynamic range compression (brightness normalization) and contrast enhancement.
Homomorphic filtering Butterworth High-frequency emphasis filter, n = 1, D = 0.6, Ka = 0.1, Kb = 0.5 Original Butterworth High-frequency emphasis filter, n = 1, D = 0.6, Ka = 0.1, Kb = 0.5 Butterworth High-pass filter, n = 1, D = 0.6
Adaptive-neighborhood Enhancement in General • Adaptive neighborhood (foreground): • Interconnected segment of pixels with certain common property with a seed pixel. (Found with seed fill.) • Properly defined segments should correspond to image features. • Found regions are extended to overlap with adjacent regions (background). • Borders of few pixels wide. • Prevents edge artifacts like reversed intensity across border. • Enhancing algorithm is performed within the combined foreground and background. • Result is applied to each seed pixel and each pixel within foreground with same value of property than seed. • Other pixels in foreground grow their own neighborhood.
Adaptive-neighborhood Contrast Enhancement • Common property: Similar gray value • To be exact: Growth tolerance . • If , all pixels connected to seed pixel with gray value between 0.95 and 1.05 times the seed pixel’s gray value are included to foreground. • All grown regions have contrast higher than independent of seed pixel’s gray value. • Worst case scenario = average foreground pixel gray value = average background pixel gray value • Weber’s ratio of 2 % (for contrast of visible features) • should be about 4 %. • Algorithm: Increase contrast to by replacing seed pixel’s value with (From equation 2.7) (From equation 2.7)
Adaptive- neighborhood contrast enhancement, growth tolerance 0.05, background depth 5 Original
Objective Assessment of Contrast Enhancement • Contrast histogram • Distribution of contrast of all possible regions obtained by seed fill algorithm. • Enhanced image should contain more counts of regions at higher contrast levels. • In practice same as more spread contrast histogram. • The second moment is used to characterize the spread
Image Enhancing- Ending Remarks • Better contrast • sharpness of detail and • visibility of features • are the targets for image enhancing. • Results can vary with each approach and image. • It can be beneficial to obtain several enhanced images with variety of approaches (as with most fields of image analysis). • Image restoration is presented in chapter 10. • Image restoration: reversing the degradation when the exact mathematical model of degradation is known.