
622 N.E.2d 548 (1993)
In the matter of Annexation Proposed by Ordinance No. X-01-89 Being an Ordinance Annexing Certain Territory Commonly Known As the Northeast Annexation Area to the City of Fort Wayne and to Include Same in Councilman's District No. 2. Certain Northeast Annexation Area LANDOWNERS, Appellants-Petitioners,
v.
CITY OF FORT WAYNE, Appellee-Respondent.
No. 02A03-9301-CV-15.
Court of Appeals of Indiana, Third District.
October 21, 1993.
Ralph R. Blume, Blume, Wyneken, Connelly, Jordan & Stucky, Fort Wayne, for appellant.
J. Timothy McCaulay, Corp. Counsel, City of Fort Wayne, Fort Wayne, for appellee.
*549 GARRARD, Judge.
Certain Northeast Area Landowners (Landowners) appeal a judgment dismissing their challenge to an annexation effort by the City of Fort Wayne (City).

FACTS AND PROCEDURAL HISTORY:
The record in this case reveals that on February 14, 1989, the Common Council of the City passed an ordinance annexing approximately 4,918 acres of land designated as the Northeast Annexation Area. Also on February 14, 1989, the Common Council passed Resolution No. R-06-89 which approved a written fiscal plan for the Northeast Annexation Area. The Mayor of the City approved and signed the ordinance and the resolution on February 15, 1989.
On April 25, 1989, Landowners filed a petition for remonstrance. On March 5, 1990, the trial court granted a partial summary judgment in favor of Landowners and an appeal ensued. This court reversed, finding that the trial court erred in its methodology for counting owners of land under IC XX-X-X-XX. City of Fort Wayne v. Landowners (1990), Ind. App., 564 N.E.2d 297 (Garrard, J., dissenting) trans. denied. The trial court, acting on this reversal, dismissed Landowners' petition for remonstrance for lack of sufficient valid signatures. Landowners appeal this dismissal.
Landowners raise several issues on appeal which we restate and consolidate as: Whether the trial court erred in dismissing Landowners' petition for remonstrance challenging the City's effort to acquire the Northeast Annexation Area.

DISCUSSION:
This case is primarily concerned with the finality of the appellate review process. Landowners in effect ask us to reopen a case that has been heard on the merits and subjected to full appellate review. Specifically, Landowners ask us to review the number of valid signatures stipulated to by the parties in the prior proceedings. We decline to do so.
In general, facts established at one stage of a proceeding, which were part of an issue on which judgment was entered and appeal taken, are unalterably and finally established as part of the law of the case and may not be relitigated at a subsequent stage. Cunningham v. Hiles (1982), Ind. App., 439 N.E.2d 669, 676. Even if the judgment is erroneous, it nevertheless becomes the law of the case and thereafter binds the parties unless successfully challenged on appeal. Id. All issues decided directly or by implication in a prior decision are binding in all further portions of the same case. Id.
We note, however, that the law of the case doctrine is a discretionary rule of practice. State v. Lewis (1989), Ind., 543 N.E.2d 1116, 1118. This doctrine expresses the practice of courts generally to refuse to reopen what has been previously decided. Id. A court has the power to revisit prior decisions of its own or of a coordinate court in any circumstance, although as a rule courts should be loathe to do so in the absence of extraordinary circumstances. Id.
In the case at bar, the parties stipulated to the number of valid signatures collected in Landowners' effort to challenge the annexation. The stipulations before the trial court were as follows:
COURT: The matter we have today is a hearing on a motion in regards to the annexation issue of areas in St. Joseph Township. So, we'll show for the record ... that Joint Exhibits Number 1, 2 and 3 have been stipulated by both the parties in evidence.[1]

*550 COURT: Anything else preliminarily before we start?
MR. McCAULAY: I think just to make clear for the record that two other stipulations are that the total number of valid signatures is 3859 and that the valid signatures do not represent 75% of the assessed value of the land.
COURT: All right. That's an agreed stipulation too, Mr. Blume, as I understand it?
MR. BLUME: 3859, Your Honor, yes.
COURT: All right.
MR. McCAULAY: And the 75  less than 75% of assessed 
COURT: And it does not include  or it does not represent 75% of the assessed value, so the issue is solely an issue of whether or not it represents more than 50% of the owners.
MR. BLUME: That's correct, Your Honor.
(R. 258, 262).
The trial court accepted the figure of 3,859 as the number of valid signatures applicable in this case and incorporated it into two of its orders.
On appeal, this court also expressly found that the parties stipulated that the total number of valid signatures on the remonstrance was 3,859. City of Fort Wayne, supra at 298. This court then ruled that, because the correct figure to compare this with was 8,026, instead of the 7,220 figure used by the trial court, Landowners did not have the signatures of a majority of the owners of land as required by IC XX-X-X-XX and, therefore, the trial court erred in finding that the remonstrance was valid. Id. Landowners' petition for rehearing was denied on February 12, 1991, and the Indiana Supreme Court denied transfer on August 22, 1991.
Landowners now seek to challenge the 3,859 figure, stating that while there were at least 3,859 valid signatures, there were 297 more whose validity remained contested and that the contested nature of these remaining signatures was also stipulated before the trial court.
While we sympathize with Landowners in this case and recognize that they may indeed have desired to contest the validity of the remaining 297 signatures, that issue ought to have been argued before the trial court and any error in computing the correct number should have been raised on direct appeal. We are faced with a factual determination that was established in the prior proceedings and was clearly part of the judgment entered. Cunningham, supra at 676. Even if the determination previously *551 made was erroneous, it is the law of the case and we will not, in the absence of extraordinary circumstances, relitigate it in this subsequent proceeding. Id.; Lewis, supra at 1118.
The trial court's order dismissing Landowners' petition for remonstrance is affirmed.
STATON and ROBERTSON, JJ., concur.
NOTES
[1]  Joint exhibit 1 contains the following:



    NORTHEAST REMONSTRANCE COUNT
                3989 (Auditor's Certification)
              +   41 (Remonstrator's List One  51)
                4030
              +   29 (Remonstrator's Tax Duplicates  65)
                4059
              +   32 (New Owners  32)
                4091
              +    9 (Affidavits  14)
                4100
              +   56 (Contract Purchasers  53)
                4156
              -   63 (Yardley Manor, Wedgewood, Chadwick II)
                4093
              -   48 (Hillsboro I  65/17 presold)
                4045
              -   43 (Concord Hill I)
                4002
              -  143 (Hillsboro II & III)
                3859
              297 Signatures subject to sewer waivers
              Remonstrator's Claim   4223
                                   -  297 (chain of title waivers)
                                     3926

(R. 259).
Joint exhibits numbers 2 and 3 are copies of certifications from the Allen County Auditor verifying 3,989 signatures from qualifying owners of taxable real estate in Allen County.
(R. 260-61).
