An Efficient Lossless ROI Image Compression Using Wavelet-Based Modified Region Growing Algorithm

3.1 Huffman Encoding Process

The Huffman coding technique is a strategy that takes a shot at the two data and image for compression. It is normally done in two phases. A statistical model is first extensively gathered; thereafter, in the second phase, the image data are encoded, as produced by the statistical model in the first phase. These codes are of variable code length utilizing an essential number of bits. This thought causes a lessening in the average code length and in this manner general size of compacted data is littler than the first.

Step 1: Read the image in the workspace of Matlab.

Step 2: Change the given color image to a gray-level image.

Step 3: The probability of images are organized in diminishing request and lower probabilities are combined, and this progression proceeds until the point that only two probabilities are left and codes are relegated by deciding that the most astounding plausible image will have a shorter length code.

Step 4: Advance Huffman encoding is performed, i.e. mapping of the code words to the compared images will bring about packed data.

3.2 MHE

The MHE algorithm consists of three significant steps: (i) Huffman code creation of original data, (ii) code conversion-based conditioning, and (iii) encoding. The following subsections explains the detailed process of the MHE algorithm.

1. Huffman code creation of original data

   1. Arrange the probabilities of the symbols (nodes) in descending order.

   2. Using the symbols of two lowest probabilities, P_A and P_B, create a new node of which these two probabilities are branches, the new node being labeled with the arithmetic sum of these two probabilities.

   3. Repeat the process using the new code instead of the original two, until only one node is left.

   4. Label each upper branch with a “0” and the lower member of each pair with a “1” or vice versa.

   5. The code for each of the original symbols is then determined by proceeding from the root of the tree to the required leaf, noting the branch label of each node traversed.

2. Code conversion of a condition-based sequence

   After generating a Huffman code for each symbol or original data (unsigned 8-bit integer value), the code conversion of the condition-based sequence is done. The process of code conversion of the condition-based sequence is as follows: initially, the original data and their code words are taken. Thereafter, the code conversion process is done by merging two symbols, i.e. number of times the selected combination of two symbols is repeated. Then, the merging process is based on the following observations:

   1. First, the merging process is applied on the selected symbols, which have to satisfy the condition, i.e. the selected symbols that satisfied this condition criterion (>1) then qualified for the merging process.

   2. Secondly, the pair that same combination of first digit of the selected pair that should not come.

   3. Third, the bit length of the first position of the pair should be lesser than the bit length of the second position of the pair.

   4. If the above three conditions are satisfied, the first position of the symbol is repeated twice and that new pair replaces the selected pair or old pair.

   5. Similarly, the above process is repeated for all selected code words.

3. Encoding

   The encoding process is done based on the combination of the symbol used in the code conversion of the merging-based sequence and the preceding symbol in the original data. The encoding process is as follows: at first, the combination of the symbols used for the code conversion process and the preceding symbol of the combination of the symbols used for the code conversion process are checked to decide whether the code formed using the code conversion process is to be considered or not. Then, three conditions (explained in the above steps) are applied and each symbol is checked in order to encode the original data. After this verification, a code is formed for the original data. The final code is the encoded data based on the MHE technique.

3.2.1 Example of the MHE Algorithm

The complete process of MHE is explained by the following example. Assume “(215) (145) (215) (145) (126) (215) (51) (45) (215) (126)” are original data and the Huffman code is formed for each symbol in the original data. The formation of the code is shown in Figure 1.

Figure 1:

Formation of Huffman Code.

Figure 1 is explained as follows: initially, the repeated letters are considered for one time and mark the frequency of the letter in the original data, i.e. the numeric term 3 below the unsigned integer value “215” represents the symbol “215” repeated three times in the original data. Thereafter, two symbols with the least frequency are taken, and zero and one are assigned to them and represent the total frequency of the two symbols below it. Similarly, this process is done by taking the next two symbols, and zeros and ones are assigned until the last step. The Huffman code is then formed for each symbol by considering the corresponding branches of zeros and ones from the last step to the first. From Figure 2, the Huffman code formed for the symbol “215” is 1; the Huffman code formed for the symbol “145” is 000; the Huffman code formed for the symbol “126” is 01; the Huffman code formed for the symbol “51” is 0011; and the Huffman code formed for the symbol “45” is 0010. Eventually, the Huffman code for the original data “(215) (145) (215) (145) (126) (215) (51) (45) (215) (126)” is “1000100001100110010101.” Figure 3 shows the direction of the Huffman code formed for each letter.

Figure 2:

After the Code Conversion Process.

Figure 3:

Direction of Huffman Code Formation.

After generating the Huffman code for each letter, the code conversion of the condition-based sequence is done by arranging the letters with the least length first. The code conversion of the merging-based sequence process is used to compress the data. In Figure 3, we obtain the frequency combination of two symbols first and the merging process is applied only on the satisfying combination. Based on the merging conditions, at first, the combination of the symbol “(215) (145)” is repeated at least two times that it only qualified for the merging process. Second, the pair of that same combination of the first digit of the selected pair “(215) (145)” should not repeat. Third, the bit length of the first position of the pair (1) should be lesser than the bit length of the second position of the pair (000). Now, the pair “(215) (145)” is qualified for the merging process. Then, the merging process is done by step 4 in the code conversion section. The new code (215) (215) is replaced ahead for (215) (145). Similarly, the code conversion process is done for all the original data. Finally, the MHE-based encoded data for the original data “(215) (145) (215) (145) (126) (215) (51) (45) (215) (126)” is “111101100110010101.” Table 1 shows the symbols with their codes after the code conversion process.

Table 1:

Segmentation Results Using the MRG Method.

3.3 SPIHT Encoding

A more efficient implementation of EZW (embedded zero wavelet) is the SPIHT algorithm [11], [17], which was represented by Shapiro. After using the wavelet transform to an image, the SPIHT algorithm partitions the decomposed wavelet into important and insignificant partitions established based on the following function:

Here, S_n(T) is a crucial set of coordinates T and C_i,j is the coefficient value at coordinate (i, j). There are two passes in the algorithm: the sorting pass and the refinement pass. The SPIHT encoding process applies three lists: LIP (list of insignificant pixels), comprising individual coefficients that have magnitudes smaller than the thresholds; LIS (list of insignificant sets), comprising the set of wavelet coefficients determined by tree structures and determined to have magnitudes smaller than the threshold; and LSP (list of significant pixels), which is a list of pixels determined to have magnitudes larger than the threshold (significant). On the above three lists, the sorting pass is executed. The maximum number of bits needed to present the largest coefficient in the spatial orientation tree is found and represented by n_max:

Those coordinates of the pixels that persist in the LIP are tested for significance by applying Eq. (2), from the sorting pass. The result is sent to the output and out of it the significant will be transferred to the LSP as well as having their sign bit output. Sets in the LIS will also get their significance examined, and, if determined significant, will be neglected and partitioned into subsets. Subsets with only one coefficient and determined to be significant will be eliminated and separated into subsets. Subsets having only one coefficient and determined to be crucial will be inserted to the LSP; otherwise, they will be inserted to the LIP. The nth most significant bit of the coefficients in the LSP is the final output in the refinement pass. The value of n is decremented, and the sorting and refinement passes are used again. These passes will continue until either the desired rate is attained or n = 0, and all nodes in the LSP have all their bit output. The latter case will cause an almost exact reconstruction so all the coefficients have been processed completely. At any time, the bit rate can be controlled exactly by the SPIHT algorithm as the output developed is in single bits and the algorithm can be completed. In terms of processing time, the decoding process follows the encoding exactly and is almost symmetrical.

3.4 Wavelet Transform

DWT is used to transform the image from its spatial domain into its frequency domain. In time, the wavelets are signals that are local in scale and normally have an irregular shape. A wavelet is a waveform of effectively determined duration that has an average value of zero. The term “wavelet” is derived from the fact that it integrates to zero; it waves up and down across the axis. For compact signal representation, several wavelets also display a property ideal. A signal can be decomposed into many shifted and scaled representations of the original mother wavelet. In component wavelets, a wavelet transform can be applied to decompose a signal. The images are decomposed into low-low (LL), low-high (LH), high-low (HL), and high-high (HH) elements, where LL is the approximate coefficient and the remaining three are detailed coefficients. Once this is caused, the coefficients of the wavelets can be decimated to neglect some of the details. For the frequency domain transforms, we utilize Haar-DWT with this suggested method. There are two operations utilizing a 2D Haar-DWT. One is the horizontal operation and the other is the vertical one. The detailed operations of 2D Haar-DWT are stated as follows [5].

Step 1: First, scan the pixels from left to right in subtraction operations on neighboring pixels and store the sum horizontal direction. Repeat this operation until all the rows are worked. The pixel sums present the low-frequency part (denoted as symbol L), while the pixel differences present the high-frequency part of the original image (denoted as symbol H).

Step 2: Second, scan the pixels from top to bottom in the vertical direction. Perform the addition and subtraction operations on neighboring pixels, and then store the sum on the top and the difference on the bottom. Repeat this operation until all the columns are processed. Finally, four sub-bands are obtained, denoted as LL, HL, LH, and HH, respectively. The LL sub-band contains the low-frequency information and it looks the same as the original image. Similarly, other bands, HL, LH, and HH, contain the high-frequency information. A wavelet function Ψ(t) has two main properties:

Figure 4:

Pixel by Pixel Representation of a 4 × 4 Image.

That is, the function is oscillatory or has a wavy appearance:

Let us consider an example for a better understanding of the 2D Haar-DWT of an image. Figure 4 illustrates the pixel-by-pixel representation of a 4 × 4 image. Figure 5 shows the output of the 2D Haar-DWT.

Figure 5:

Example of 2D-Haar DWT of an Image.

3.5 DCT

In multimedia standards, DCT is an orthogonal transformation that is very widely applied in image compression and is widely accepted. DCT belongs to a family of 16 trigonometric transformations. The type 2 DCT transmutes a block of image size N × N having pixel intensities S(n₁, n₂) into a transform array of coefficients S(K₁, K₂), depicted by the following equation:

where K₁, K₂, n₁, n₂ = 0, 1, …, N − 1, and

The transformed array S(K₁, K₂) found through Eq. (5) is also of the size N × N, same as that of the original image block. In the directions of n₁ and n₂, it should be mentioned here that the transform-domain indices K₁ and K₂ denote the spatial frequencies, respectively. K₁ = K₂ = 0 corresponds to the average or the direct current component, and all the remaining ones are the alternating current components that correspond to higher spatial frequencies as K₁ and K₂ increase.

4.1 Segmentation of ROI and non-ROI

The ROI is the most significant portion of a medical image. It comprises the most valuable data of the medical image and should not undergo any modification. There can be numerous disjoint ROIs in a medical image and numerous manners exist to describe the ROI in a medical image. Here, a segmentation algorithm is used to detect the ROI from the input image. Segmentation is one of the most important parts of the complete image processing cycle, and it forms a very helpful and an essential part of object detection. In this paper, to segment the ROI from the input image, we utilize the MRG algorithm. Consider the input image I(i, j) that has a size of 256 × 256. Initially, we segment the ROI from the input image. The projected MRG technique segments the input image with respect to a point called a seed. In the region growing segmentation, the chief point is to regulate the initial seed points. A seed point is the commencement stage for region growing, and its selection is significant for the segmentation solution. The technique of mathematical morphology is engaged in order to attain an initial seed point. The detailed procedure of the projected region growing-based image segmentation procedure is elucidated below.

Step 1: Consider the input image I(i, j), which has a size of 256 × 256. Here, first, we split the image into a number of blocks, Bⁱ. Each block has one center pixel and a number of neighborhood pixels.

Step 2: Then, we set the intensity threshold, (TIN).

Step 3: For every block Bⁱ, proceed with the subsequent processes in step 7 until the number of blocks reached the total number of blocks for an image.

Step 3(a): Find the histogram H of each pixel in Bⁱ.

Step 3(b): Regulate the most frequent histogram of the B^ith block and signify it as F^H.

Step 3(c): Prefer any pixel according to F^H and allocate that pixel as seed point that has the intensity IN_p.

Step 3(d): Deliberate the adjacent pixel having the intensity IN_n.

Step 3(e): Find the intensity difference of those pixels p and n:

Step 3(f): If DIN≤TIN, then add the consistent pixel to the region and the region is grown; else, move to step 3(h).

Step 3(g): Check whether all pixels are added to the region. If true, go to step 2, then go to step 3(h).

Step 3(h): Re-estimate the region and detect the new seed points and do the procedure in step 3(a).

Step 4: Stop the whole procedure.

With the help of this MRG procedure, the input images are segmented. The segmented image output is displayed in Figure 7.

Figure 7:

Segmentation Output.

(A) Input image. (B) Segmented ROI image. (C) Segmented non-ROI image.

4.2 Image Compression Algorithm

The primary intention of our research is to compress the medical image efficiently. The objective of image compression is to reduce the irrelevance and redundancy of image data in order to store or transmit data in an efficient form. Here, segmented regions are effectively compressed by employing wavelet transform and encoding techniques. The proposed image compression algorithm is given below:

1. Input: original image OI[i.j].

2. Output: compressed image CI[i.j].

Step 1: Segmentation using region growing algorithm

The first step of image compression is segmentation. For segmentation, in this paper, we utilize an MRG algorithm. Initially, the input magnetic resonance image I[i.j] is clustered into two segments such as ROI image IROI[i,j] and non-ROI image Inon-ROI[i.j] using the MRG algorithm. After the ROI detection process, the major task is to compress the input image or medical image I[i.j] with the lossless version. To obtain this result, we have individually compressed each segmented images as [ROI]_c and [non-ROI]_c.

Step 2: Computation of [ROI]_c

1. To compute [ROI]_c, DCT is first applied to select DCT coefficients; then, SPIHT is applied to bit streams with the aim of doing lossless compression in DCT coefficients.

2. After the cosine transform, the SPIHT encoding algorithm is used to generate a compressed ROI image [ROI]_c. The compressed ROI image [ROI]_c is present in the bit stream format. The SPIHT encoder converts the image components into the bit stream. SPIHT works by partitioning the wavelet-decomposed image into significant and insignificant partitions based on the following function:

   (8) Sn(τ)={1,if max(i,j)∈τ{ci,j}≥2n0,Otherwise,

   where 2ⁿ is the threshold, S_n(τ) is a significant set of coordinates, and τ and c_i,j are the coefficient values at coordinates i, j. In this algorithm, three ordered lists are used to store the significance information during set partitioning: LIS, LIP, and LSP. The detailed explanation of the SPIHT procedure is given in Section 3.1. Finally, we obtain the compressed ROI image [ROI]_c from the encoding process.

Step 3: Computation of [non-ROI]_c

1. To compute [non-ROI]_c, we first decompose the image I_non-ROI[i, j] into sub-bands using DWT, which improves the compression ratio. The divided sub-bands are HH, LL, HL, and LH. From the four sub-bands, the HL sub-band is chosen for the encoding process.

2. Thereafter, the non-ROI image I_non-ROI[i.j] is encoded using MHE, which is used to compress the bit stream. The detailed explanation of the MHE approach is explained in Section 3.2. Finally, we obtain the compressed non-ROI image, [non-ROI]_c.

Step 4: Evaluate compression ratio I^Com[i.j] using [ROI]_c and [non-ROI]_c

From the above steps (2) and (3), we individually calculate the compression ratio using Eq. (9). Finally, the compressed medical image or input image I^Com[i.j] is obtained from Eq. (10).

4.3 Image De-compression Algorithm

The decompression process is exactly the inverse of the compression process. First, the bit stream of the ROI mask code is decoded using the SPIHT decoding decompression algorithm, and that of the non-ROI code is decompressed by the corresponding modified Huffman decoding method. The proposed image de-compression stage involves following significant steps:

1. Input: compressed bit stream I^Com[i.j].

2. Output: compressed image I^Dec[i.j].

Step 1: Calculation of [non-ROI]^Dec

The modified Huffman decoding and inverse DWT are used to compute [non-ROI]^Dec from the compressed image [non-ROI]_c. The reverse operation of merge Huffman coding and DWT is performed to obtain [non-ROI]_dc.

Step 2: Calculation of [ROI]_dc

Here, the decompressed ROI image [ROI]^Dec is calculated from the compressed image [ROI]_c through the reverse operation of DCT and SPIHT decoder. Finally, [ROI]^Dec is obtained using inverse DCT and SPIHT decoder.

Step 4: Calculate decompressed image I^Dec[i, j] using OR operation

To calculate the decompressed image I^Dec[i, j], we merge the three decompressed regions as in steps 1 and 2. Finally, the resultant decompressed image I^Dec[i, j] is obtained using logical OR operation as Eq. (11):

where I^Dec[i, j] is the decompressed output image, [ROI]^Dec is the decompressed ROI, and [non-ROI]^Dec is the decompressed non-ROI.

5.1 Evaluation Matrices

In this paper, the performance is analyzed based on famous metrics such as compression ratio, PSNR, cross-correlation, average difference, and NAE, defined as follows:

Compression ratio: The image compression ratio is the ratio between the uncompressed size and compressed size, as follows:

PSNR: The description of PSNR is given in the following formulas:

where D_i[i.j]_w and D_i[i.j]_h are the width and height of the decompressed image, O_I[i.j]_xy is the original image pixel value at coordinate (x, y), D_i[i.j]_xy is the decompressed image pixel value at coordinate (x, y), and Emax2 is the largest energy of the image pixels (i.e. E_max = 255 for 256 gray-level images).

Cross-correlation: The cross-correlation between the original image O_I[i.j] and decompressed image D_i[i.j] is

Average difference: The average difference (AD) of the input and decompressed image is given by

NAE: The NAE is given by

5.2 Experimental Results

In this paper, we proposed a medical image compression approach. At first, the input magnetic resonance image is segmented into two regions (ROI and non-ROI) using the MRG algorithm. Then, we compress the ROI and non-ROI separately. Finally, we calculate the compressed image from the input image. Here, we analyze the performance of the proposed system using two phases: segmentation and compression. The visual results of the segmentation phase are given in Table 1, and the Possibilistic Fuzzy C-means clustering (PFCM)-based segmentation results are given in Table 2.

Table 2:

Segmentation Result Using the PFCM Method.

5.3 Comparative Analysis

In this section, we compare our proposed image compression approach with the PFCM-based image compression approach. In our proposed approach, at first, we segment the input image into two regions using the MRG algorithm. Then, we compress the ROI using DWT with SPIHT encoding and the non-ROI using DCT with modified Huffman encoding method. To prove the effectiveness of the proposed approach, the proposed method is compared with PFCM-based image compression. Here, for segmentation, the PFCM algorithm is used. PFCM is a combination of fuzzy C-means and possibilistic C-means. Table 3 shows the performance of the proposed approach against existing metrics.

Table 3 shows the comparative analysis of the proposed against existing methods for the compression stage. For experimentation, here we used five magnetic resonance images. When analyzing Table 1, our proposed approach achieves the maximum PSNR of 39.73 dB for using image 1, 38.65 dB for using image 2, 44.29 dB for using image 3, 41.98 dB for using image 4, and 46.69 dB for using image 5. Consequently, the PFCM-based compression obtains the maximum PSNR of 31.00 dB for using image 1, 30.78 dB for using image 2, 36.05 dB for using image 3, 32.68 dB for using image 4, and 34.55 dB for using image 5. Similarly, our proposed approach achieves the maximum compression ratio of 3.88 dB for using image 1, 1.68 dB for using image 2, 2.30 dB for using image 3, 2.50 dB for using image 4, and 2.46 dB for using image 5. Consequently, PFCM-based compression obtains the maximum compression of 3.58 dB for using image 1, 3.39 dB for using image 2, 2.16 dB for using image 3, 1.02 dB for using image 4, and 1.05 dB for using image 5. From the table, we clearly understand that our proposed approach achieves the maximum PSNR and compression ratio compared to PFCM-based compression. Table 2 shows the performance of the segmentation stage. In this proposed approach, we used the MRG algorithm for segmentation. When analyzing Table 4, our proposed approach achieves the maximum accuracy of 99.36% for using image 1, 99.27% for using image 2, 99.48% for using image 3, 99.21% for using image 4, and 98.25% for using image 5. From the result, we clearly understand that our proposed approach achieves the better result.