CN102790882B - Encoding method of remote sensing image - Google Patents

Abstract

The invention discloses an encoding method of a remote sensing image. The method comprises the following steps: performing preprocessing on an original remote sensing image, then performing discrete wavelet transformation and quantization processing on the original remote sensing image; dividing a quantized sub-brand coefficient into encoding blocks in smaller sizes, performing plane expansion of significant bit with the same bit depth on each encoding block, and then sequentially ordering each encoding block from small to large; performing embedded bit plane encoding and MQ (multiplier-quotient) arithmetic encoding on each encoding block; calculating rate distortion-slope and accumulation rate of each channel of each bit plane of each ordered encoding block and determining whether to stop accumulating or not; calculating threshold of the rate-distortion slope and screening the rate-distortion slope of remaining channels based on the threshold; and carrying out Tier2 encoding. By adopting the encoding method provided by the invention, coding redundancy of Tier1 can be greatly reduced, and searching range of threshold value of an optimal-rate distortion-slope and optimal cut-off point during the Tier2 encoding is narrowed, so that the encoding efficiency and speed of the remote sensing image are remarkably improved and the complexity is reduced.

Description

A kind of coding method of remote sensing images

Technical field

The invention belongs to image processing field, particularly a kind of coding method of remote sensing images.

Background technology

Along with the raising of the resolution of remote sensing images, remote sensing image data amount also increases thereupon, makes the real-time Transmission of data and storage become more and more difficult, thereby the effective image compression particular importance that just seems.

Remote Sensing Image Compression coding adopts JPEG2000 compression and coding standard conventionally at present.The coding method complexity of JPEG2000 standard is very high, and its complexity major part is to come from embedded block coding (EBCOT) bit rate control method that band optimization is blocked.EBCOT is encoded by Tier 1 and Tier 2 encodes, and two parts form, and wherein, Tier 1 coding accounts for the computing time of JPEG2000 encoder 45%-60%, and the amount of calculation that reduces Tier 1 will greatly reduce the processing time of coded system; After Tier 2 parts adopt compression, rate-distortion optimization rate distribution method (Post Compression Rate Distortion is called for short PCRD) is carried out Rate Control.But this method need to be encoded to all data of Tier 1, and stores all encoding code streams.And in the time of low code check, the passage that has a large amount of coded scannings is can not be included in final code stream.

The deficiency existing for PCRD method, many scholars have proposed new method, as document [Auli-Llinas F, Serra-Sagrista J, Monteagudo-Pereira J, et al.Efficient rate control for JPEG2000coder and decoder[J] .Proc.IEEE DCC, Mar.2006, 1:282-291.] [Qin becomes with document, Chen Zhiyun, Yu Kun, Zhou Yan. the research [J] of the rate control algorithm based on JPEG2000. computer application and software, 2011, the 28th volume (the 2nd phase): 76-80.] propose algorithm be the rate control algorithm based on interlacing scan coding pass, the patent No. is 200410026016.6 the JPEG2000 method of rate control blocking in real time, the patent No. be 200710018190.X based on the preallocated JPEG2000 adaptive rate control of code check system and method etc., these papers and invention have all improved the code efficiency of JPEG2000 significantly, but Rate Control is accurate not, the Y-PSNR (PSNR) of Recovery image has obvious decline.Document [Kim T., Kim H.M., Tsai P.S., et al.Memory efficient progressive rate-distortion algorithm for JPEG2000[J] .IEEE Trans.on Circuits and Systems for Video Technology.2005, 15 (1): 181-187.] and document [Wang Chao, Wang Jiong. a kind of effectively JPEG2000 rate control algorithm [J]. Donghua University's journal (natural science edition), 2011, the 37th volume (the 1st phase): 76-80.] propose method reduced encoding calculation amount and memory space, but coding redundancy is larger under high code check, and increase minimum slope search arithmetic.

Based on above analysis, the inventor carries out Improvement to existing coding method, and this case produces thus.

Summary of the invention

Object of the present invention, be to provide a kind of coding method of remote sensing images, it can greatly reduce the redundancy that Tier 1 encodes, also dwindle the scope of searching for optimum rate-distortion slope threshold value and optimum point of cut-off when Tier 2 encodes simultaneously, thereby improve significantly code efficiency and the speed of remote sensing images, reduce complexity.

In order to reach above-mentioned purpose, solution of the present invention is:

A coding method for remote sensing images, comprises the steps:

(1) original remote sensing images are carried out to preliminary treatment, comprise the burst processing of conversion process, pixel value electrical level shift processing and the image of color component;

(2) carry out wavelet transform to carrying out pretreated remote sensing images through step (1);

(3) continue remote sensing images to carry out quantification treatment;

(4) carry out Tier 1 and encode, specifically comprise the following steps:

(41) be first divided into the encoding block of reduced size by quantizing sub-band coefficients, each encoding block is made to the significance bit planar development of the identical bits degree of depth, then according to significance bit number of planes order from small to large, each encoding block is sorted successively, if the equal and opposite in direction of significance bit number of planes, sorts successively by former order; Each encoding block is carried out to embedded bit-plane coding and MQ arithmetic coding;

(42) calculate in the encoding block after sequence rate-distortion slope and the cumulative code check of each passage in each bit plane, and judge whether to stop accumulative total;

(43) the threshold value λ of calculation rate distortion slope _nopt;

(44) according to the value of rate-distortion slope, remaining channel is screened;

(5) carrying out Tier 2 encodes.

The particular content of above-mentioned steps (42) is: from first encoding block, and the rate-distortion slope S of each passage in each bit plane in the encoding block after calculating sequence _jwith cumulative code check; When passage of each accumulative total, whether relatively more cumulative code check is greater than target bit rate, no longer the passage in remaining encoding block after remaining passage in present encoding piece and current code block is added up if be greater than, forwards next step to, otherwise continue coding next passage, wherein rate-distortion slope S _jformula be:

$S_j=\frac{D_{j-1}-D_j}{R_j-R_{j-1}}$

Wherein, j is channel position, R _jand R _j-1represent to be respectively accumulated to j and (j-1) accumulative total code check when passage, D _jand D _j-1represent respectively j and (j-1) distortion that produces when passage.

The particular content of above-mentioned steps (43) is:

1. calculate the least significant bit (LSB) number of planes of the encoding block needs of having encoded;

2. the slope of last coding pass in more each encoding block of having encoded, obtains the minimum rate-distortion slope S in the encoding block of having encoded ₁;

3. compare the size of trying to achieve compression multiple by code check and the target bit rate of accumulation, thereby obtain threshold value λ _nopt, expression formula is as follows:

${\mathrm{\&lambda;}}_{\mathrm{nopt}}=\left\{\begin{array}{cc}{S}_1,& R_{\max }\&le;R<{2R}_{\max }\\ 2^{\mathrm{numbps}},& {2R}_{\max }\&le;R<{4R}_{\max }\\ 3^{\mathrm{numbps}},& R\&GreaterEqual;{4R}_{\max }\end{array}\right.---\left(3\right)$

Wherein, numbps is expressed as the significance bit number of planes of last encoding block of having encoded, and R is expressed as cumulative code check, R _maxbe expressed as target bit rate; R _max≤ R<2R _maxwhile representing low compression multiple, get less threshold value; R>=4R _maxwhile representing high compression multiple, get larger threshold value.

The particular content of above-mentioned steps (44) is:

Last encoding block of having encoded from step (42) starts, and continues the rate-distortion slope S of passage in the remaining encoding block of calculation procedure (42) _jwith cumulative code check R; Obtain threshold value λ by formula (3) _noptwith S _jcompare, if the rate-distortion slope S of the coding pass calculating _jbe greater than zero and be less than or equal to threshold value λ _nopt, abandon and be less than or equal to λ _noptall coding passes below, carry out the calculating of next encoding block; Otherwise the rate-distortion slope of next passage in this code block is calculated in continuation.

Adopt after such scheme, the present invention to encoding block in the time that Tier 1 encodes, percent of pass distortion slope threshold value is as threshold value, can block the passage of being lost in a large number in the time that Tier 2 encodes, method provided by the present invention is in the situation that remote sensing images keep original signal to noise ratio, can greatly reduce amount of calculation and the memory space of Tier 1 coded portion, also dwindled the scope of searching for optimum rate-distortion slope threshold value and optimum point of cut-off when Tier 2 encodes simultaneously, amount of calculation and memory space can reduce Remote Sensing Image Compression coding time, reduce complexity, improve code efficiency and speed.

Brief description of the drawings

Fig. 1 is the comparison diagram of the average peak signal to noise ratio difference of 8 width remote sensing images of method provided by the present invention and PCRD method;

Fig. 2 is method provided by the present invention and the percentage schematic diagram of the average computation amount ratio of 8 width remote sensing images of PCRD method;

Fig. 3 is the percentage schematic diagram of the average memory space of 8 width remote sensing images of method provided by the present invention and PCRD method.

Embodiment

Below with reference to accompanying drawing, technical scheme of the present invention is elaborated.

First, when Tier 1 encodes while the object of the invention is for Remote Sensing Image Coding based on JPEG2000 standard, there is the problem of a large amount of calculating redundancies and storage resources waste, a kind of coding method of effective remote sensing images has been proposed, in JPEG2000 standard base, Tier 1 coding is improved: first according to the size of significance bit number of planes, the coded sequence of adjusting encoding block, makes it count to least significant bit (LSB) number of planes from most significant digit plane and encodes successively; Then according to the relation of compression multiple and target bit rate, the threshold value of a self adaptation formula calculation rate distortion slope of proposition.The improved foundation of the present invention program, 1) compression multiple of remote sensing images is larger, the target bit rate that image distributes is fewer, in the time that cumulative code check is more than or equal to target bit rate, the significance bit number of planes obtaining is relatively higher, if can calculate threshold value according to the height of significance bit number of planes, just can block ahead of time the coding pass of the HFS that can be dropped in the time of Tier 2 Rate Control.2) compression multiple of remote sensing images is larger, and the target bit rate that image distributes is fewer, and the optimum rate-distortion slope obtaining at Tier 2 is just larger.Therefore, when compression multiple is larger, threshold value also should be larger, to lose more redundant channel.Therefore, the threshold value obtaining with self adaptation formula can be blocked redundant channel in advance, by losing the coding pass that is less than this threshold value, make remote sensing images in the situation that almost keeping original signal to noise ratio, greatly reduce redundancy when Tier 1 encodes, also dwindled when Tier 2 encodes and searched for the scope of optimum rate-distortion slope threshold value and optimum point of cut-off, thereby reduced amount of calculation and the memory space of remote sensing images simultaneously.

The coding method of a kind of remote sensing images provided by the present invention, comprises the steps:

(1) original remote sensing images are carried out to preliminary treatment, comprise the burst processing of conversion process, pixel value electrical level shift processing and the image of color component;

(2) carry out wavelet transform to carrying out pretreated remote sensing images through step (1);

Wavelet transformation is to be low-frequency band coefficient LL and multiple high frequency band coefficient LH, HL, HH by picture breakdown.It is all level and smooth sub-band coefficients that LL is expressed as horizontal and vertical direction; It is level and smooth that LH is expressed as horizontal direction, and vertical direction is the sub-band coefficients of details; It is contrary with LH that HL represents, horizontal direction is details, and vertical direction is level and smooth sub-band coefficients; HH is expressed as the sub-band coefficients that horizontal and vertical direction is all details.Therefore low-frequency band coefficient LL is the concentrated frequency band of image energy, and high frequency band coefficient HL, LH, HH are mainly edge, texture and profile, and wavelet coefficient is all very little.

(3) continue remote sensing images to carry out quantification treatment;

Quantification is that the sub-band coefficients precision obtaining after wavelet transformation is adjusted, and changes a bit number that wavelet sub-band coefficient is required of expression by adjusting the size of quantization step, to adjust and to control the processing procedure of compressed image code check.The wavelet coefficient obtaining after wavelet transformation can obtain quantized value with formula below:

Wherein, q _b(u, v) is the value after quantizing, X _b(u, v) is wavelet sub-band coefficient, the quantization step that Δ b is wavelet sub-band, sign (X _b(u, v)) expression wavelet sub-band coefficient X _bthe sign symbol of (u, v), u, v represent respectively wavelet sub-band coefficient X _bthe row-coordinate of (u, v) (matrix) and row coordinate.

(4) carry out Tier 1 and encode, specifically comprise the following steps:

(41) sequence

First quantification sub-band coefficients is divided into the encoding block of reduced size, the height of encoding block roomy little be 2 power integer value within the scope of 4-1024, and high be widely ly long-pendingly less than 4096, general code block size can be made as 64 × 64 or the coded block size of 32 × 32, Jasper software default be 64 × 64;

Each encoding block is made to the significance bit planar development of the identical bits degree of depth, then, according to the size of each code block significance bit number of planes numbps, each encoding block is sorted to minimum numbps successively from maximum numbps; If the equal and opposite in direction of significance bit number of planes numbps, sorts successively by former order;

Then, each encoding block is carried out to embedded bit-plane coding and MQ arithmetic coding, embedded bit-plane coding is from highest significant position plane (highest significant position that comprises coefficient), finish to least significant bit planes (least significant bit that comprises coefficient), a context is determined in each position, based on context estimated probability, then sends position and its probability to MQ arithmetic encoder; MQ arithmetic encoder and JBIG, JPEG adopt QM encoder substantially similar, are all improving one's methods of Q encoder, and MQ encoder is also applied to jbig standard.

(42) calculate cumulative code check

From first encoding block, the rate-distortion slope S of each passage in each bit plane in the encoding block after calculating sequence _jwith cumulative code check; When passage of each accumulative total, whether relatively more cumulative code check is greater than target bit rate, no longer the passage in remaining encoding block after remaining passage in present encoding piece and present encoding piece is added up if be greater than, forwards next step to, otherwise continue coding next passage, wherein rate-distortion slope S _jformula as the formula (2):

$S_j=\frac{D_{j-1}-D_j}{R_j-R_{j-1}}---\left(2\right)$

Wherein, j is channel position, R _jand R _j-1represent to be respectively accumulated to j and (j-1) accumulative total code check when passage, D _jand D _j-1represent respectively j and (j-1) distortion that produces when passage;

(43) the threshold value λ of calculation rate distortion slope _nopt

1. calculate the least significant bit (LSB) number of planes numbps of the encoding block needs of having encoded, because encoding block is by the descending sequence successively of significance bit number of planes, so only need find the significance bit number of planes of last encoding block of coded block;

2. obtain the minimum rate-distortion slope S in the encoding block of having encoded ₁, the only slope of last coding pass in the more each encoding block of having encoded of need;

3. the large I of compression multiple is compared and is tried to achieve by code check and the target bit rate of accumulation, thereby obtains threshold value λ _nopt, expression formula is as follows:

${\mathrm{\&lambda;}}_{\mathrm{nopt}}=\left\{\begin{array}{cc}{S}_1,& R_{\max }\&le;R<{2R}_{\max }\\ 2^{\mathrm{numbps}},& {2R}_{\max }\&le;R<{4R}_{\max }\\ 3^{\mathrm{numbps}},& R\&GreaterEqual;{4R}_{\max }\end{array}\right.---\left(3\right)$

Wherein, numbps is expressed as the significance bit number of planes of last encoding block of having encoded, and R is expressed as cumulative code check, R _maxbe expressed as target bit rate; R _max≤ R<2R _maxwhile representing low compression multiple, get less threshold value; R>=4R _maxwhile representing high compression multiple, get larger threshold value.

(44) according to the value of rate-distortion slope, remaining channel is screened

Last encoding block of having encoded from step (42) starts, and continues the rate-distortion slope S of passage in the remaining encoding block of calculation procedure (42) _jwith cumulative code check R.Obtain threshold value λ by formula (3) _noptwith S _jcompare.If the rate-distortion slope S of the coding pass calculating _jbe greater than zero and be less than or equal to threshold value λ _nopt, abandon and be less than or equal to λ _noptall coding passes below, carry out the calculating of next encoding block; Otherwise the rate-distortion slope of next passage in this code block is calculated in continuation.All encoding blocks complete after above process, then carry out Tier 2 and encode.

The inventive method, in the time that Tier 1 encodes, first according to the size of significance bit number of planes, is adjusted the coded sequence of encoding block, makes it count to minimum planes number from dominant bit plane and encodes successively; Then larger according to the compression multiple of image, to distribute this fewer feature of target bit rate, has proposed a self adaptation formula, the threshold value that the rate-distortion slope of being obtained is encoded as Tier 1.By losing the coding pass that is less than this threshold value, make remote sensing images in the situation that almost keeping original signal to noise ratio, greatly reduce the redundancy that Tier 1 encodes, also dwindled Tier 2 and searched for the scope of optimum rate-distortion slope threshold value and optimum point of cut-off, thereby reduced amount of calculation and the memory space of remote sensing images simultaneously.

(5) Tier 2 encodes

The input of 2 coding stages of Tier is the set of the each channel coding data of each code block of Tier 1 stage generation.Tier 2 is responsible for pressing mass segregation and packing and process of input code flow, and with form, data packet group is woven to last output code flow in sequence.In order to make compressed bit stream have qualitative scalability, by the encoding code stream of all Bit-Plane Encoding passages of each code block, by it, the serviceability to picture quality is divided into some levels to method, is called quality layers.The contribution that each layer comprises each code block.Rate Control part will determine should comprise which coding pass of each code block in each layer of encoding code stream.

From above step, encoding block in the time that Tier 1 encodes, the rate-distortion slope threshold value λ obtaining by formula (3) _noptas threshold value, can block in advance a large amount of coding passes of finally being lost in the time that Tier 2 encodes, this will greatly reduce amount of calculation and the memory space of Tier 1 coded portion, has also dwindled the scope that Tier 2 searches for optimum rate-distortion slope thresholding and optimum point of cut-off simultaneously.Therefore, the present invention is no matter be that the aspect such as scramble time or the loss of resource is all better than the PCRD method of recommending in traditional JPEG2000.

In order to verify the effect of the inventive method, the Jasper software that in use JPEG2000 standard, PART5 provides is realized Rate Control in this paper and is improved one's methods.The present embodiment is the remote sensing images that differ in size from 30 width, to choose at random 8 width images to test.All image selected parameters of this experiment are the same, use 5/3 small echo, 6 layers of wavelet decomposition, and the size of encoding block is 64 pixel × 64 pixels.Table 1 has provided the comparative result of the PSNR value of the inventive method and PCRD method, and △ PSNR represents the difference of two kinds of method PSNR.

Table 1

To describe from the content of many aspects his-and-hers watches 1 below.

(1) Y-PSNR of image, table 1 is that the PSNR value of the inventive method and PCRD method compares.As can be seen from Table 1, under different code checks, the inventive method is compared with PCRD method, and the PSNR of image slightly declines, and the amplitude major part of decline is in 0.1dB, and maximum is 0.151dB only.But under some code check, be slightly better than PCRD method, the amplitude of improvement is at 0.002-0.017dB.And in the time of 1.0bpp, PSNR remains unchanged.

For the ease of comparing, Fig. 1 has shown in the time of different code check, the mean P SNR difference of 8 width remote sensing images.Can know and find out under the condition of different code checks from Fig. 1, the mean P SNR difference of the inventive method and PCRD method is all less than 0.05dB, and the image quality loss that therefore also can find out the inventive method is very little.

(2) amount of calculation of method, the inventive method is that the coding pass quantity of encoding with Tier 1 is weighed.Fig. 1 is under different code check conditions, and 8 width remote sensing images are realized the percentage of the average computation amount of Tier 1 part after Rate Control by this method and PCRD method.As seen from the figure, the inventive method is not almost changing under the prerequisite of signal to noise ratio, has greatly reduced the quantity of coding pass.In the time of 0.25bpp, just drop to 29.93% number of channels of PCRD method.In the time of 0.0625bpp, drop to 18.13% number of channels of PCRD method.Visible, the inventive method can effectively reduce the amount of calculation that Tier 1 encodes.

(3) memory space of method, the inventive method is weighed with the code stream byte number of storage in Tier 1 coding.Under different code checks, Fig. 2 is the percentage that the inventive method and PCRD method realize the average memory space of Tier 1 part after Rate Control.As seen from the figure, along with the decline of code check, the memory space of Tier 1 coded portion also declines thereupon.In the time of 0.0625bpp, 0.125bpp, 0.25bpp, 0.5bpp and 1bpp, the memory space mean value that the method for proposition accounts for PCRD method is 7.81%, 12.16%, 20.51%, 36.54% and 57.53%.Therefore, greatly reduced the required amount of ram of Remote Sensing Image Coding.

Compare the existing remote sensing coding method based on JPEG2000 standard, the inventive method can realize efficient coding control.The inventive method has utilized the significance bit number of planes of encoding block to be these fewer two features of target bit rate of dull downward trend and the larger image of compression multiple, by the adaptive threshold value that calculates of formula proposing, block the coding pass that is less than threshold value, make remote sensing images in the situation that keeping original signal to noise ratio, greatly reduce the redundancy that Tier 1 encodes, also dwindled the scope of searching for optimum rate-distortion slope threshold value and optimum point of cut-off when Tier 2 encodes, thereby reduced significantly amount of calculation and the memory space of remote sensing images simultaneously.

Above embodiment only, for explanation technological thought of the present invention, can not limit protection scope of the present invention with this, every technological thought proposing according to the present invention, and any change of doing on technical scheme basis, within all falling into protection range of the present invention.

Claims (3)

1. a coding method for remote sensing images, is characterized in that comprising the steps:

(1) original remote sensing images are carried out to preliminary treatment, comprise the burst processing of conversion process, pixel value electrical level shift processing and the image of color component;

(2) carry out wavelet transform to carrying out pretreated remote sensing images through step (1);

(3) continue remote sensing images to carry out quantification treatment;

(4) carry out Tier1 coding, specifically comprise the following steps:

(41) be first divided into the encoding block of reduced size by quantizing sub-band coefficients, each encoding block is made to the significance bit planar development of the identical bits degree of depth, then according to significance bit number of planes order from big to small, each encoding block is sorted successively, if the equal and opposite in direction of significance bit number of planes, sorts successively by former order; Each encoding block is carried out to embedded bit-plane coding and MQ arithmetic coding;

(42) calculate in the encoding block after sequence rate-distortion slope and the cumulative code check of each passage in each bit plane, and judge whether to stop accumulative total;

(43) the threshold value λ of calculation rate distortion slope _nopt;

The particular content of described step (43) is:

1. calculate the least significant bit (LSB) number of planes of the encoding block needs of having encoded;

2. the slope of last coding pass in more each encoding block of having encoded, obtains the minimum rate-distortion slope S in the encoding block of having encoded ₁;

3. compare the size of trying to achieve compression multiple by code check and the target bit rate of accumulation, thereby obtain threshold value λ _nopt, expression formula is as follows:

${\mathrm{\&lambda;}}_{\mathrm{nopt}}=\left\{\begin{array}{cc}{S}_1,& R_{\max }\&le;R<{2R}_{\max }\\ 2^{\mathrm{numbps}},& {2R}_{\max }\&le;R<{4R}_{\max }\\ 3^{\mathrm{numbps}},& R\&GreaterEqual;4R_{\max }\end{array}\right.---\left(1\right)$

Wherein, numbps is expressed as the significance bit number of planes of last encoding block of having encoded, and R is expressed as cumulative code check, R _maxbe expressed as target bit rate; R _max≤ R<2R _maxwhile representing low compression multiple, get less threshold value; R>=4R _maxwhile representing high compression multiple, get larger threshold value;

(44) according to the value of rate-distortion slope, remaining channel is screened;

(5) carry out Tier2 coding.

2. the coding method of a kind of remote sensing images as claimed in claim 1, it is characterized in that: the particular content of described step (42) is: from first encoding block, the rate-distortion slope S of each passage in each bit plane in the encoding block after calculating sequence _jwith cumulative code check; When passage of each accumulative total, whether relatively more cumulative code check is greater than target bit rate, no longer the passage in remaining encoding block after remaining passage in present encoding piece and current code block is added up if be greater than, forwards next step to, otherwise continue coding next passage, wherein rate-distortion slope S _jformula be:

$S_j=\frac{D_{j-1}-D_j}{R_j-R_{j-1}}$

Wherein, j is channel position, R _jand R _j-1represent to be respectively accumulated to j and (j-1) accumulative total code check when passage, D _jand D _j-1represent respectively j and (j-1) distortion that produces when passage.

3. the coding method of a kind of remote sensing images as claimed in claim 1, is characterized in that: the particular content of described step (44) is:

Last encoding block of having encoded from step (42) starts, and continues the rate-distortion slope S of passage in the remaining encoding block of calculation procedure (42) _jwith cumulative code check R; Obtain threshold value λ by expression formula (1) in step (43) _noptwith S _jcompare, if the rate-distortion slope S of the coding pass calculating _jbe greater than zero and be less than or equal to threshold value λ _nopt, abandon and be less than or equal to λ _noptall coding passes below, carry out the calculating of next encoding block; Otherwise the rate-distortion slope of next passage in this code block is calculated in continuation.